Measuring Space Perimeter and Area Class 9 MCQ Maths Chapter 6

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MCQ on Measuring Space Perimeter and Area Class 9

Class 9 Maths Measuring Space Perimeter and Area MCQ

Choose the correct option from the given options (Use π = \(\frac {22}{7}\) unless otherwise stated):

Question 1.
The circumference of a circle is 66 cm, its radius is:
(a) 10 cm
(b) 11 cm
(c) 10.5 cm
(d) 11.5 cm
Solution:
(c) 10.5 cm

Explanation:
C = 2πr
∴ 66 = 2 × \(\frac {22}{7}\) × r
⇒ r = \(\frac{66 \times 7}{2 \times 22}=\frac{21}{2}\)
= 10.5 cm.
So, the radius for the given circle will be 10.5 cm.

Question 2.
Length of an arc of a circle of radius 21 cm, which subtends an angle 60° at the centre, is:
(a) 22 cm
(b) 11cm
(c) 10.5 cm
(d) 21 cm
Solution:
(a) 22 cm

Explanation:
l = \(\frac{\theta}{360}\) × 2πr = \(\frac{60}{360}\) × 2 × \(\frac {22}{7}\) × 21 = 22 cm
So, the length of the arc of the given circle will be 22 cm.

Question 3.
The perimeter of a sector of a circle of radius 28 cm which subtends a central angle 45° is:
(a) 28 cm
(b) 56 cm
(c) 22 cm
(d) 78 cm
Solution:
(d) 78 cm

Explanation:
Perimeter of a sector = 2r + \(\frac {22}{7}\) × 2πr
= 56 + 22 = 78 cm.

Question 4.
The ratio of the circumferences of two circles is 3 : 7. The ratio of their radii is:
(a) 2 : 3
(b) 3: 7
(c) 7 : 3
(d) 3 : 2
Solution:
(b) 3: 7

Explanation:
Let r₁ and r₂ be the radii of the two circles.
Ratio of their circumferences = \(\frac{1}{2}\)
⇒ \(\frac{1}{2}\) so, the required ratio of their radii = 3 : 7.

Question 5.
Areas of two circles are in the ratio 16 : 25. The ratio of their radii is:
(a) 25 : 16
(b) 16 : 25
(c) 5 : 4
(d) 4 : 5
Solution:
(d) 4 : 5

Explanation:
Let r₁ and r₂ be the radii of the two circles.
Ratio of their areas = \(\frac{\pi r_1^2}{\pi r_2^2}=\frac{r_1^2}{r_2^2}\)
\(\left(\frac{r_1}{r_2}\right)^2=\frac{16}{25} \Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{16}{25}}=\frac{4}{5}\), so the required ratio of their radii = 4:5.

Measuring Space Perimeter and Area MCQ Class 9

Question 6.
Area of a square whose side has length 5 cm is:
(a) 25 cm²
(b) 36 cm²
(c) 16 cm²
(d) 49 cm²
Solution:
(a) 25 cm²

Explanation:
Area of the square = a², where ‘a’ is the length of its side.
Area = 5 × 5 = 25 cm²

Question 7.
Length of a rectangle is 10 cm and its width is 7 cm. The area of the rectangle is:
(a) 34 cm²
(b) 65 cm²
(c) 70 cm²
(d) 17 cm²
Solution:
(c) 70 cm²

Explanation:
Area of the rectangle = l × b, where 7’ is the length and ‘b’ is the breadth.
Here, l = 10 cm and 5 = 7 cm
Area of the rectangle = 10 × 7 = 70 cm².

Question 8.
Base length of a parallelogram is 24 cm and its height is 20 cm. The area of the parallelogram is:
(a) 440 cm²
(b) 480 cm²
(c) 470 cm²
(d) 420 cm²
Solution:
(b) 480 cm²

Explanation:
Area of the parallelogram = Base x Height.
Here, base = 24 cm and height = 20 cm
Area of the parallelogram = 24 × 20 = 480 cm².

Question 9.
In the following figure, BC = 8 cm, AD is the median, AM = 3 cm.

The area of ∆ADB is:
(a) 4 cm²
(b) 8 cm²
(c) 7 cm²
(d) 6 cm²
Solution:
(d) 6 cm²

Explanation:
Since, AD is the median
Hence, CD = DB = \(\frac{B C}{2}=\frac{8}{2}\) = 4 cm
Therefore, Area of ΔADB = \(\frac{1}{2}\) × 4 × 3 = 6 cm².

Question 10.
The area of a triangle whose sides are 6 cm, 8 cm and 10 cm, is:
(a) 14 cm²
(b) 18 cm²
(c) 24 cm²
(d) 30 cm²
Solution:
(c) 24 cm²

Explanation:
Here, a = 6 cm, b = 8 cm and c = 10 cm.
s = \(\frac{a+b+c}{2}=\frac{6+8+10}{2}=\frac{24}{2}\) =12,
Using Heron’s formula, we obtain
Area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{12(12-6)(12-8)(12-10)}\)
= \(\sqrt{12 \times 6 \times 4 \times 2}\) = 24 cm².

Question 11.
Area of a triangle is 24cm2. Its altitude is 12 cm. Its base is:
(a) 12 cm
(b) 18 cm
(c) 4 cm
(d) 6 cm
Solution:
(c) 4 cm

Explanation:
Area of the triangle = \(\frac{1}{2}\) × Base × Altitude
⇒ \(\frac{1}{2}\) × Base × 12 = 24 (given)
Base = 4 cm.

Question 12.
Perimeter of a square is 12 cm. Its area is:
(a) 16 cm²
(b) 9 cm²
(c) 25 cm²
(d) 36 cm²
Solution:
(b) 9 cm²

Explanation:
Perimeter of the square = 4 × side ⇒ 4 × side = 12 cm (given)
side = \(\frac{12}{4}\) = 3 cm
Now, area of the square = (side)² = (3)² = 9 cm²

Question 13.
In the following figure, ∆ABC is inscribed in a circle of radius 6 cm. AB = 6 cm.BC = 7 cm and CA = 8 cm. The area of the ∆ABC is:

(a) 24 cm²
(b) 28 cm²
(c) 42 cm²
(d) 14 cm²
Solution:
(d) 14 cm²

Explanation:
Area of the ∆ABC = \(\frac{a b c}{4 \mathrm{R}}\)
Here, a = 7 cm, 6 = 8 cm, c = 6 cm
Area of ∆ABC = \(\frac{7 \times 8 \times 6}{4 \times 6}\) = 14 cm².

Question 14.
In the following figure, circle of radius 3 cm is inscribed in ∆ABC, in which AB = 8 cm, BC = 9 cm and CA = 10 cm. The area of ∆ABC is:

(a) 24.5 cm²
(b) 40.5 cm²
(c) 42.5 cm²
(d) 14.5 cm²
Solution:
(b) 40.5 cm²

Explanation:
Area of the ∆ABC = \(\frac{1}{2}\)
Here, a = 9 cm, 6 = 10 cm, c = 8 cm
Area of ∆ABC = \(\frac{1}{2}\) = 40.5 cm² .

Question 15.
A Cyclic 4-gon has sides of lengths 6 cm. 8 cm, 12 cm and 12 cm. Its area is:
(a) 7\(\sqrt{143}\) cm²
(b) 12\(\sqrt{143}\) cm²
(c) 6\(\sqrt{143}\) cm²
(d) 8\(\sqrt{143}\) cm²
Solution:
(a) 7\(\sqrt{143}\) cm²

Explanation:
Here, let a = 6, cm b = 8, cm c = 12 cm, d = 12 cm.
∴ s = \(\frac{a+b+c+d}{2}=\frac{6+8+12+12}{2}\) = 19
Area of the Cyclic 4-gon = \(\sqrt{(s-a)(s-b)(s-c)(s-d)}\)
= \(=\sqrt{(19-6)(19-8)(19-12)(19-12)(s-d)}\)
= \(\sqrt{(13)(11)(7)(7)}\)
= 7\(\sqrt{143}\) cm².

Question 16.
In the following figure, the area of ∆UNI is:

(a) 40 cm²
(b) 20 cm²
(c) 42 cm²
(d) 22 cm²
Solution:
(b) 20 cm²

Explanation:
Area of the AUNI = \(\frac{1}{2}\) × Area of rectangle PINK
Here, a = 8 cm, b = 5 cm,area of rectangle = l × b = 8 × 5 = 40 cm²
Area of AUNI = \(\frac{1}{2}\) × (40) = 20 cm².

Question 17.
The circumference of a circle is 22 cm, its radius is:
(a) 11 cm
(b) 7 cm
(c) 22 cm
(d) 14 cm
Solution:
(b) 7 cm

Question 18.
Length of an arc of a circle of radius 21 cm, which subtends an angle 120° at the centre, is:
(a) 22 cm
(b) 11cm
(c) 44 cm
(d) 33 cm
Solution:
(c) 44 cm

Question 19.
The perimeter of a sector of a circle of radius 14 cm which subtends a central angle 60° is:
(a) 42 \(\frac{1}{4}\) cm
(b) 14 \(\frac{1}{3}\) cm
(c) 14 \(\frac{2}{3}\) cm
(d) 42 \(\frac{2}{3}\) cm
Solution:
(d) 42 \(\frac{2}{3}\) cm

Question 20.
The ratio of the circumferences of two circles is 4 : 5. The ratio of their radii is:
(a) 4 : 5
(b) 4:9
(c) 5 : 4
(d) 9 : 4
Solution:
(a) 4 : 5

Question 21.
Areas of two circles are in the ratio 4 : 9. The ratio of their radii is:
(a) 2 : 9
(b) 2 : 3
(c) 3 : 2
(d) 9 : 2
Solution:
(b) 2 : 3

Question 22.
Area of a square whose side has length 12 cm is:
(a) 81 cm²
(b) 169 cm²
(c) 144 cm²
(d) 125 cm²
Solution:
(c) 144 cm²

Question 23.
Length of a rectangle is 6 cm and its width is 4.5 cm. The area of the rectangle is:
(a) 27 cm²
(b) 24 cm²
(c) 32 cm²
(d) 28 cm²
Solution:
(a) 27 cm²

Question 24.
Base length of a parallelogram is 12 cm and its height is 7.25 cm. The area of the parallelogram is:
(a) 87 cm²
(b) 84 cm²
(c) 42 cm²
(d) 64 cm²
Solution:
(a) 87 cm²

Question 25.
In the following figure, BC = 12 cm, AD is the median, AM = 5 cm.

The area of AADB is:
(a) 4 cm²
(b) 8 cm²
(c) 15 cm²
(d) 7.5 cm²
Solution:
(c) 15 cm²

Question 26.
In a triangle, a = 12, b = 6,c = 7, s =?
(a) 12.5
(b) 25
(c) 6.25
(d) 3.125
Solution:
(a) 12.5

Question 27.
Area of an equilateral triangle whose side is 6 cm, is:
(a) 3√3 cm²
(b) 9√3 cm²
(c) 3√2 cm²
(d) 6√3 cm²
Solution:
(b) 9√3 cm²

Question 28.
The area of a triangle whose sides are 5 cm, 7 cm and 8 cm, is:
(a) 5√3 cm²
(b) 10√3 cm²
(c) 10 cm²
(d) 30 cm²
Solution:
(b) 10√3 cm²

Question 29.
Area of a triangle is 24 cm². Its base is 12 cm. Its altitude is:
(a) 12 cm
(b) 18 cm
(c) 4 cm
(d) 6 cm
Solution:
(c) 4 cm

Question 30.
Perimeter of a square is 20 cm. Its area is:
(a) 16 cm²
(b) 9 cm²
(c) 25 cm²
(d) 36 cm²
Solution:
(c) 25 cm²

Question 31.
In the following figure, ∆PQR is inscribed in a circle of radius 3 cm. PQ = 4 cm,QR = 7 cm and RP = 9 cm. The area of the ∆PQR is:

(a) 21 cm²
(b) 28 cm²
(c) 42 cm²
(d) 14 cm²
Solution:
(a) 21 cm²

Question 32.
In the following figure, circle of radius 3 cm is inscribed in ∆ABC, AB = 4 cm, BC = 7 cm and CA = 9 cm. The area of ∆ABC is:

(a) 30 cm²
(b) 15 cm²
(c) 45.5 cm²
(d) 45 cm²
Solution:
(a) 30 cm²

Question 33.
A Cyclic 4-gon has sides of lengths 9 cm, 12 cm, 12 cm and 7 cm. Its area is:
(a) 7\(\sqrt{143}\) cm²
(b) 12\(\sqrt{143}\) cm²
(c) 6\(\sqrt{143}\) cm²
(d) 8\(\sqrt{143}\) cm²
Solution:
(d) 8\(\sqrt{143}\) cm²

Question 34.
In the following figure, the area of AUNI is:

(a) 11.25 cm²
(b) 45 cm²
(c) 22.5 cm²
(d) 22 cm²
Solution:
(c) 22.5 cm²

Measuring Space Perimeter and Area Class 9 Assertion and Reason Questions

Direction: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following options.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Question 1.
Assertion (A): Length of an arc of a circle of radius 14 cm subtending an angle 90° at the centre is 11 cm.
Reason (R): Area of the circle of radius 14 cm is 616 cm².
Solution:
(d) Assertion (A) is false but Reason (R) is true.

Explanation:
Length of the arc = \(\frac{\theta}{360}\) × 2πr
= \(\frac{90^{\circ}}{360^{\circ}}\) × 2 × \(\frac{22}{7}\) × 14 = 22 cm.
Hence, Assertion (a) is false. Area of the circle = πr² = \(\frac{22}{7}\) × (14)²
= \(\frac{22 \times 14 \times 14}{7}\)
= 616 cm²
Thus, Reason (R) is true.

Question 2.
Assertion (A): Ratio of areas of two circles, whose radii are in the ratio 4 : 3 is 16 : 9.
Reason (R): Ratio of circumferences of two circles, whose radii are in the ratio 2 : 5 is 4 : 25.
Solution:
(c) Assertion (A) is true but Reason (R) is false.

Explanation:
Ratio of areas of two circles =
\(\frac{\pi r_1^2}{\pi r_2^2}=\left(\frac{r_1}{r_2}\right)^2=\left(\frac{4}{3}\right)^2=\frac{16}{9}\) = 16 : 9
So, Assertion (A) is true.
Ratio of circumferences of two circles =\(\frac{r_1}{r_2}\)
= \(\frac{2}{5}\) = 2:5.
So, Reason (R) is false.

Question 3.
Assertion (A): Area of a triangle whose sides are a, b and c, is given by \(\sqrt{(s-a)(s-b)(s-c)}\).
Reason (R) : s = \(\frac{a+b+c}{2}\), is the semi perimeter of the triangle.
Solution:
(d) Assertion (A) is false but Reason (R) is true.

Explanation:
Area of a triangle whose sides are a, b and c, is given by \(\sqrt{s(s-a)(s-b)(s-c)}\). So, Assertion (A) is false.
s = \(\frac{a+b+c}{2}\) is the semi perimeter of the triangle.
So, Reason (R) is true.

Question 4.
Assertion (A): Perimeter of the sector of a circle of radius 7 cm and central angle 120° is \(\frac{86}{3}\) cm.
Reason (R): Perimeter of the sector of a circle of radius ‘r’ is given by 2r + \(\frac{\theta}{360}\) × 2πr.
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:
Perimeter of the sector =
2r + \(\frac{1}{2}\) × 2πr = 2 × 7 + \(\frac{120^{\circ}}{360^{\circ}}\) × 2 × \(\frac{22}{7}\) × 7
= 14 + \(\frac{44}{3}=\frac{86}{3}\)
So, Assertion (A) is true.
Perimeter of the sector = 2r + \(\frac{\theta}{360}\) × 2πr
So, Reason (R) is true and Reason (R) is the correct explanation of the Assertion (A).

Question 5.
Assertion (A): Area of the semicircle = \(\frac{1}{2}\).
Reason (R): Semicircle subtends an angle 180° at the centre.
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:
Area of the semicircle =
\(\frac{\theta}{360} \times \pi r^2=\frac{180^{\circ}}{360^{\circ}} \times \pi r^2=\frac{1}{2} \times \pi r^2 .\)
Therefore, Assertion (A) is true.
Semicircle is half of the circle so, it subtends 180° at the centre.
So, Reason (R) is true and Reason (R) explains the existence of Assertion (A).

Question 6.
Assertion (A): Length of an arc of a circle of radius 42 cm subtending an angle 60° at the centre is 22 cm.
Reason (R): Circumference of the circle of radius 42 cm is 264 cm².
Solution:
(d) Assertion (A) is false but Reason (R) is true.

Question 7.
Assertion (A): Ratio of areas of two circles, whose radii are in the ratio 2 : 7 is 4 : 14.
Reason (R): Ratio of circumferences of two circles, whose radii are in the ratio 2 : 5 is 2 : 5.
Solution:
(d) Assertion (A) is false but Reason (R) is true.

Question 8.
Assertion (A): Perimeter of a semicircle = d + \(\frac{\pi d}{2}\), where ‘d’ is the diameter of the circle.
Reason (R): Length of semicircle of a circle = πd, where ‘d’ is the diameter of the circle.
Solution:
(c) Assertion (A) is true but Reason (R) is false.

Question 9.
Assertion (A): Area of a triangle whose sides are 3 cm, 4 cm and 5 cm is 6 cm².
Reason (R): If s is the semi-perimeter of the triangle having sides of lengths a, b and c, then the value of s = a + b + c.
Solution:
(c) Assertion (A) is true but Reason (R) is false.

Question 10.
Assertion (A): A triangle of sides 3 cm, 4 cm and 5 cm is inscribed in a circle, the radius of the circle is 2.5 cm.
Reason (R): The circumradius ‘R’ of the circumcircle inscribing a triangle having sides a, b and c, is given by \(\frac{a b c}{4 \mathrm{~A}}\), where A is the area of the triangle.
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).