Practice Problems on Surface Area and Volume of a Sphere with Solutions

Problem 1: A spherical water tank has a radius of 5 meters. Calculate the volume of water it can hold.

Solution:

Volume of sphere = 4/3πr³

So, radius = 5m

Volume = 4/3 × π × r× r × r

= 4/3 × 3.14 × 5 × 5 × 5

= 523.33 m³

Problem 2: Volume of a sphere is 288πm³. Calculate the diameter of the sphere.

Solution:

Volume of a sphere is 288π m³

According to formula,

⇒ 4/3 × π × r × r × r = 288π

⇒ r = 6m

So, diameter of the sphere = 2r = 12 m.

Problem 3: Given a sphere of diameter of 20m. Find the volume of the sphere.

Solution:

Given,

• Diameter(D) = 20 m
• Radius(r) = D/2 = 10 m

Volume = 4/3πr³

= 4/3 × π × 10 × 10 × 10

= 4186 m³

So, volume of the sphere of diameter 20 m is 4186 m³

Problem 4: Given a sphere of radius 10m. Find the surface area of the sphere.

Solution:

Given,

• Radius = 10 m
• Volume = 4πr²

= 4 × π × 10 × 10

= 1256m²

So, surface area of the sphere of radius 10m is 1256 m².

Problem 5: Given a sphere of diameter 14m. Find the surface area of the sphere.

Solution:

Given,

• Diameter = 14 m
• Radius = 7 m
• Volume = 4πr²

= 4 × π × 7 × 7

= 615.44 m²

So, surface area of the sphere of radius 5m is 1256 m².

Problem 6: Given a hemisphere of radius 5m. Find the surface area of the hemisphere.

Solution:

Given,

• Radius = 5 m
• Volume = 2πr²

= 2 × π × 5 × 5

= 157 m²

So, surface area of the hemisphere of radius 5m is 157 m².

Problem 7: Given a solid hemisphere of radius 8m. Find the surface area of the solid hemisphere.

Solution:

Given,

• Radius = 7 m
• Volume = 3πr²

= 3 × π × 7 × 7

= 461.58 m²

So, surface area of the solid hemisphere of radius 7m is 461.58 m².

Problem 8: Given a sphere whose surface area is 5544m². Find the diameter sphere.

Solution:

Given,

• Surface Area = 5544 cm²

⇒ 4π×r×r = 5544

⇒ 4× 3.14 × r×r = 5544

⇒ r×r = 441

⇒ r = 21m

So, diameter of the sphere is 42 m.

Problem 9: Given a hemisphere of radius 5m. Find the volume of the hemisphere.

Solution:

Given,

• Radius = 5m
• Volume = 2/3πr³

= 2/3 × π × 5 × 5 × 5

= 261.66 m³

So, volume of the hemisphere of radius 5 m is 261.66 m³.

Problem 10: Given a hemisphere of radius 8m. Find the volume of the hemisphere.

Solution:

Given,

• Radius = 8 m
• Volume = 2/3πr³

= 2/3 × π × 8 × 8 × 8

= 1071.78 m³

So, volume of the hemisphere of radius 8m is 1071.78 m³

In this article, we are going to study about an important chapter of school mathematics. This article will explain concepts related to the sphere and solve questions and unsolved questions.