**Chapter 9 Surface Area and Volume Practice Set 9.3**

Chapter 9 Surface Area and Volume Practice Set 9.3

**Question 1.Find the surface areas and volumes of spheres of the following radiii. 4 cmii. 9 cmiii. 3.5 cm (π = 3.14)i. Given: Radius (r) = 4 cmTo find: Surface area and volume of sphereSolution:**

**ii. Given: Radius (r) = 9 cmTo find: Surface area and volume of sphereSolution:**

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 cmTo find: Surface area and volume of sphereSolution:**

**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 cmTo find: Curved surface area and total surface area of hemisphereSolution:**

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 sphereSolution:**

i. Surface area of sphere = 4πr

^{2}

∴ 2826 = 4 x 3.14 x r

^{2}

2826 = 282600 = 900

∴ r

^{2}= 225

= 43 x 3.14 x 15

^{3}

= 43 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 =22/7)Given: Volume of sphere = 38808 cubic cm.To find: Surface area of sphereSolution:**

∴ 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 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 hemisphereSolution:**

= 9000 x 3

∴ r

^{3}= 27000

= 30 cm

ii. Diameter = 2r

= 2 x 30 = 60 cm

∴ The diameter of the hemisphere is 60 cm.