## Maharashtra State Board Class 9 Maths Solutions Chapter 9 Surface Area and Volume Practice Set 9.3

Question 1.

Find the surface areas and volumes of spheres of the following radii

i. 4 cm

ii. 9 cm

iii. 3.5 cm (π = 3.14)

i. Given: Radius (r) = 4 cm

To find: Surface area and volume of sphere

Solution:

Surface area of sphere = 4πr^{2}

= 4 x 3.14 x 4^{2}

∴ Surface area of sphere = 200.96 sq.cm

Volume of sphere = \(\frac { 4 }{ 3 }\)πr^{3}

= \(\frac { 4 }{ 3 }\) x 3.14 x 4^{2}

∴ Volume of sphere = 267.95 cubic cm

ii. Given: Radius (r) = 9 cm

To find: Surface area and volume of sphere

Solution:

Surface area of sphere = 4πr^{2}

= 4 x 3.14 x 9^{2}

∴ Surface area of sphere = 1017.36 sq.cm

∴ Volume of sphere = 3052.08 cubic cm

iii. Given: Radius (r) = 3.5 cm

To find: Surface area and volume of sphere

Solution:

Surface area of sphere = 4πr^{2}

= 4 x 3.14 x (3.5)^{2}

∴ Surface area of sphere = 153.86 sq.cm

Volume of sphere = \(\frac { 4 }{ 3 }\) πr^{3}

= \(\frac { 4 }{ 3 }\) x 3.14 x (3.5)^{3}

∴ Volume of sphere = 179.50 cubic cm

Question 2.

If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area, (π = 3.14)

Given: Radius (r) = 5 cm

To find: Curved surface area and total surface area of hemisphere

Solution:

i. Curved surface area of hemisphere = 2πr^{2}

= 2 x 3.14 x 5^{2}

= 2 x 3.14 x 25

= 50 x 3.14

= 157 sq.cm.

ii. Total surface area of hemisphere = 3πr^{2}

= 3 x 3.14 x 5^{2}

= 235.5 sq.cm.

∴ The curved surface area and totai surface area of hemisphere are 157 sq.cm, and 235.5 sq.cm, respectively.

Question 3.

If the surface area of a sphere is 2826 cm^{2} then find its volume. (π = 3.14)

Given: Surface area of sphere = 2826 sq.cm.

To find: Volume of sphere

Solution:

i. Surface area of sphere = 4πr^{2}

∴ 2826 = 4 x 3.14 x r^{2}

2826 = 282600 = 900

∴ \( r^{2}=\frac{2826}{4 \times 3.14}=\frac{282600}{4 \times 314}=\frac{900}{4}\)

∴ r^{2} = 225

∴ r = \(\sqrt { 225 }\) … [Taking square root on both sides]

= 15 cm

ii. Volume of sphere = \(\frac { 4 }{ 3 }\) πr^{3}

= \(\frac { 4 }{ 3 }\) x 3.14 x 15^{3}

= \(\frac { 4 }{ 3 }\) x 3.14 x 15 x 15 x 15

= 4 x 3.14 x 5 x 15 x 15

= 14130 cubic cm.

∴ The volume of the sphere is 14130 cubic cm.

Question 4.

Find the surface area of a sphere, if its volume is 38808 cubic cm. (π = \(\frac { 22 }{ 7 }\))

Given: Volume of sphere = 38808 cubic cm.

To find: Surface area of sphere

Solution:

∴ r^{3} = 441 x 21 = 21 x 21 x 21

∴ r = 21 cm … [Taking cube root on both sides]

ii. Surface area of sphere = 4πr^{2}

= 4 x \(\frac { 22 }{ 7 }\) x 21

= 4 x \(\frac { 22 }{ 7 }\) x 21 x 21

= 4 x 22 x 3 x 21

= 5544 sq.cm.

∴ The surface area of sphere is 5544 sq.cm.

Question 5.

Volume of a hemisphere is 18000π cubic cm. Find its diameter.

Given: Volume of hemisphere = 1 8000π cubic cm.

To find: Diameter of the hemisphere

Solution:

i. Volume of hemisphere = \(\frac { 2 }{ 3 }\) πr^{3}

= 9000 x 3

∴ r^{3} = 27000

∴ r = \(\sqrt [ 3 ]{ 27000 }\) … [Taking cube root on both sides]

= 30 cm

ii. Diameter = 2r

= 2 x 30 = 60 cm

∴ The diameter of the hemisphere is 60 cm.