Practice Problem on Surface Area and Volume of a Cube

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

Important Related Formulas related to Cube

Total Surface Area of Cube= 6 (Side)²

Lateral Surface Area of Cube = 4 (Side)²

Volume of a Cube= (Side)³

Diagonal of a Cube = √3(Side)

Perimeter of Cube = 12 × Side

Practice Problems with Solutions.

Q1: The side length of a cube is 6 meters. Calculate the perimeter of the cube.

Solution:

To find the perimeter of a cube, apply the following formula

p = 12 × s

Given,

s = 6m

So, perimeter = 12 × s

⇒ Perimeter = 12 × 6

⇒ Perimeter = 72 m.

So, the perimeter of the cube is 72 m.

Q2: A cube has a perimeter of 108 meters. Determine its side.

Solution:

To find the side of a cube, apply the following formula

P = 12 × s

Given,

P = 108m

So, perimeter = 12 × s

⇒ 108 = 12 × s

⇒ s = 9m

So, the side of the cube is 72 m.

Q3: Given a cube with each side measuring 6 meters, calculate diagonal of the cube.

Solution:

To find the diagonal of a cube, apply the following formula

d = √3(s)

Given,

s = 6m

So, diagonal = √3(s)

= √3 × 6

= 6√3m.

So, the perimeter of the cube is 6√3m.

Q4: If diagonal of a cube is 27 m, then find its side.

Solution:

To find the side of a cube, apply the following formula

d = √3(s)

Given,

d = 27m

So, diagonal = √3(s)

⇒ 27= √3 × s

⇒ s = 9√3

So, the side of the cube is 9√3m

Q5: Calculate the volume of a cube that has sides of 6 meters each.

Solution:

To find the volume of a cube, apply the following formula

V = s³

Given,

s = 6m

So, volume = s³

= 6 × 6 × 6

216m³

So, the volume of the cube is 216m³

Q6: For a cube with 343 m³ volume, find the side of the cube.

Solution:

To find the side of a cube, apply the following formula

V = s³

Given,

v = 343m³

So, volume = s³

⇒ 343 = s × s × s

⇒ s = 7m

So, the side of the cube is 7m

Q7: John wants to wrap a gift box shaped like a cube with side length 4 inches. How much wrapping paper does he need in total?

Solution:

Since the gift box is in the shape of a cube

So, it has total of 6 faces.

Area of each faces = 4×4

= 16

So, total area required = area of each face × number of faces

= 16× 6

= 96.

So, John would required 96inches² of wrapping paper.

Q8: A water tank is in the shape of a cube with each side measuring 10 feet. What is the volume of water it can hold in gallons?

Solution:

Given,

side = 10feet.

Volume = s × s× s

So, to calculate the volume of water that can be hold in gallons is

= 10 × 10 × 10

= 1000

So, total volume of water that can be hold in gallons is 1000 feet³.

Q9: Sarah is painting the walls of her room, which is in the shape of a cube with side length 12 feet. How much paint does she need to cover all the walls?

Solution:

Given,

no of faces = 6 faces

Area of each face = s × s

12 × 12 = 144 square feet

So, the total surface area of the walls is 6 × 144 = 864 square feet.

Q10: A cube-shaped block of ice with a side length of 6 inches is melting. If it melts completely, how much water will it become?

Solution:

Given,

side = 6inch

volume = s × s × s

= 6 × 6 × 6

= 216 cubic inches

So, the volume of melted water is 216 cubic inches.

Unsolved Questions

Q1: A cube has a side length of 5 cm. Determine the surface area and volume of the cube.

Q2: If the side length of a cube is doubled from its original size of 3 meters, what are the new surface area and volume?

Q3: Compare two cubes where one has a side length of 4 inches and the other has a side length of 6 inches. Calculate the surface area and volume for each, and find the ratio of their surface areas and volumes.

Q4: A cubic water tank holds 27,000 liters of water. Assuming that 1 cubic meter equals 1000 liters, find the length of a side of the tank. Then, calculate the surface area of this tank.

Q5: A company manufactures cubic containers that are 10 feet on each side. If the cost to coat the surface area of the container is $2 per square foot, calculate the total cost to coat one container.

Q6: A set of three cubes have side lengths of 2 cm, 4 cm, and 6 cm, respectively. Calculate the total surface area and combined volume of these three cubes.

Q7: Design a cubic frame that has a volume of 1 cubic meter. Determine the surface area of this frame.

Q8: A large cubic shipping container has a volume of 64 cubic feet. Determine the side length and surface area of the container.

Q9: If the side length of a cube is reduced by 50% from its original length of 8 meters, what will be the new volume and surface area?

Q10: You need to paint all six sides of a cube-shaped room where each side is 12 feet long. If one gallon of paint covers 300 square feet, how many gallons of paint are required to paint the entire room?