Practice Problems on Surface Area and Volume of a Sphere

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.

Important Formulas Related to Sphere

A sphere is a three-dimensional figure that resembles a ball and various formulas related to a sphere are:

Volume of a Sphere (V)	4/3πr3
Surface Area of a Sphere (A)	4πr2
Surface Area of a Hemisphere	2πr2
Surface Area of a Solid Hemisphere	3πr2
Volume of a Hemisphere	2/3πr3

where,

• r is Radius of the Hemisphere

Practice Problems on Surface Area and Volume of a Sphere

Q1. A spherical water tank has a radius of 8 meters. Calculate the volume of water it can hold.

Q2. Volume of a sphere is 512π m³. Calculate the diameter of the sphere.

Q3. Given a sphere of diameter of 30 meters. Find the volume of the sphere.

Q4. Given a sphere of radius 12 meters. Find the surface area of the sphere.

Q5. Given a sphere of diameter 18 meters. Find the surface area of the sphere.

Q6. Given a hemisphere of radius 6 meters. Find the surface area of the hemisphere.

Q7. Given a solid hemisphere of radius 10 meters. Find the surface area of the solid hemisphere.

Q8. Given a sphere whose surface area is 7392πm². Find the diameter of the sphere.

Q9. Given a hemisphere of radius 7 meters. Find the volume of the hemisphere.

Q10. Given a hemisphere of radius 12 meters. Find the volume of the hemisphere.

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

FAQs on Surface Area and Volume of a Sphere

Does sphere comes under two-dimensional geometry or three-dimensional geometry?

Sphere comes under the category of three-dimensional geometry.

If we are given the radius of a sphere, then find the diameter of the sphere.

To find the diameter of a sphere, we use the formula,

Diameter = 2 × Radius of Sphere

Can we find radius of sphere if we are given the surface area value of the sphere?

Yes, we can calculate the radius of sphere if the surface area of the sphere is given.

Find surface area of solid hemissphere which have radius = 4 cm.

To calculate the surface area of a solid hemisphere we use the formula, Surface Area = 3πr²

Surface Area = 3 × 3.14 × 4 × 4

= 48 × 3.14 = 150.72 cm²

Find radius of a sphere whose surface area is 154 cm².

To calculate radius of a sphere we use the formula, Surface Area = 4πr²

⇒ 154 = 4 × 3.14 × r × r

⇒ r×r = 12.26

⇒ r = 3.5 cm