## Maharashtra State Board Class 9 Maths Solutions Chapter 9 Surface Area and Volume Practice Set 9.1

Question 1.

Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.

Given: For cuboid shape box of medicine,

length (l) = 20 cm, breadth (b) = 12 cm and height (h) = 10 cm.

To find: Surface area of vertical faces and total surface area of the box

Solution:

i. Surface area of vertical faces of the box

= 2(l + b) x h

= 2(20+ 12) x 10

= 2 x 32 x 10

= 640 sq.cm.

ii. Total surface area of the box

= 2 (lb + bh + lh)

= 2(20 x 12+ 12 x 10 + 20 x 10)

= 2(240 + 120 + 200)

= 2 x 560

= 1120 sq.cm.

∴ The surface area of vertical faces and total surface area of the box are 640 sq.cm, and 1120 sq.cm, respectively.

Question 2.

Total surface area of a box of cuboid shape is 500 sq.unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box?

Given: For cuboid shape box,

breadth (b) = 6 unit, height (h) = 5 unit Total surface area = 500 sq. unit.

To find: Length of the box (l)

Solution:

Total surface area of the box = 2 (lb + bh + lh)

∴ 500 = 2 (6l + 6 x 5 + 5l)

∴ \(\frac { 500 }{ 2 }\) = (11l + 30)

∴ 250= 11l + 30

∴ 250 – 30= 11l

∴ 220 = 11l

∴ 220 = l

∴ \(\frac { 220 }{ 11 }\) = l

∴ l = 20 units

∴ The length of the box is 20 units.

Question 3.

Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.

Given: Side of cube (l) = 4.5 cm

To find: Surface area of all vertical faces and the total surface area of the cube

Solution:

i. Area of vertical faces of cube = 4l^{2}

= 4 (4.5)^{2} = 4 x 20.25 = 81 sq.cm.

ii. Total surface area of the cube = 6l^{2}

= 6 (4.5)^{2}

= 6 x 20.25

= 121.5 sq.cm.

∴ The surface area of all vertical faces and the total surface area of the cube are 81 sq.cm, and 121.5 sq.cm, respectively.

Question 4.

Total surface area of a cube is 5400 sq. cm. Find the surface area of all vertical faces of the cube.

Given: Total surface area of cube = 5400 sq.cm.

To find: Surface area of all vertical faces of the cube

Solution:

i. Total surface area of cube = 6l^{2}

∴ 5400 = 6l^{2}

∴ \(\frac { 5400 }{ 6 }\) = l^{2}

∴ l^{2} = 900

ii. Area of vertical faces of cube = 4l^{2}

= 4 x 900 = 3600 sq.cm.

∴ The surface area of all vertical faces of the cube is 3600 sq.cm.

Question 5.

Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5 m and 1.15 m respectively. Find its length.

Given: Breadth (b) = 1.5 m, height (h) = 1.15 m

Volume of cuboid = 34.50 cubic metre

To find: Length of the cuboid (l)

Solution:

Volume of cuboid = l x b x h

∴ 34.50 = l x b x h

∴ 34.50 = l x 1.5 x 1.15

= 20

∴ The length of the cuboid is 20 m.

Question 6.

What will be the volume of a cube having length of edge 7.5 cm ?

Given: Length of edge of cube (l) = 7.5 cm

To find: Volume of a cube

Solution:

Volume of a cube = l^{2}

= (7.5)^{3}

= 421.875 ≈ 421.88 cubic cm

∴The volume of the cube is 421.88 cubic cm.

Question 7.

Radius of base of a cylinder is 20 cm and its height is 13 cm, find its curved surface area and total surface area, (π = 3.14)

Given: Radius (r) = 20 cm, height (h) = 13 cm

To find: Curved surface area and

the total surface area of the cylinder

Solution:

i. Curved surface area of cylinder = 2πrh

= 2 x 3.14 x 20 x 13

= 1632.8 sq.cm

ii. Total surface area of cylinder = 2πr(r + h)

= 2 x 3.14 x 20(20 + 13)

= 2 x 3.14 x 20 x 33 = 4144.8 sq.cm

∴ The curved surface area and the total surface area of the cylinder are 1632.8 sq.cm and 4144.8 sq.cm respectively.

Question 8.

Curved surface area of a cylinder is 1980 cm^{2} and radius of its base is 15 cm. Find the height of the cylinder. (π = \(\frac { 22 }{ 7 }\))

Given: Curved surface area of cylinder = 1980 sq.cm., radius (r) = 15 cm

To find: Height of the cylinder (h)

Solution:

Curved surface area of cylinder = 2πrh

∴ 1980 = 2 x \(\frac { 22 }{ 7 }\) x 15 x h

∴ \(h=\frac{1980 \times 7}{2 \times 22 \times 15}\)

∴ h = 21 cm

∴ The height of the cylinder is 21 cm.