Volume And Surface Area Formula Quiz

1. What is the volume of a cube with side length 3 cm?

27 cm³

9 cm³

18 cm³

54 cm³

The volume of a cube is calculated by multiplying the side length by itself three times (length x width x height). Here, the side length is 3 cm. Applying this formula, the calculation for the volume of the cube is 3 cm x 3 cm x 3 cm = 27 cm³. This calculation determines the total cubic space enclosed within the cube, which is an essential geometric property when considering the capacity or content that the cube can hold. This formula, straightforward yet foundational, illustrates how dimensions directly scale the volume in geometric shapes.

Explanation

The volume of a cube is calculated by multiplying the side length by itself three times (length x width x height). Here, the side length is 3 cm. Applying this formula, the calculation for the volume of the cube is 3 cm x 3 cm x 3 cm = 27 cm³. This calculation determines the total cubic space enclosed within the cube, which is an essential geometric property when considering the capacity or content that the cube can hold. This formula, straightforward yet foundational, illustrates how dimensions directly scale the volume in geometric shapes.

2. What is the volume of a rectangular prism with length 6 cm, width 4 cm, and height 3 cm?

72 cm³

24 cm³

288 cm³

144 cm³

To calculate the volume of a rectangular prism, multiply its length, width, and height together using the formula V = l x w x h, where l is the length, w is the width, and h is the height. For a prism with dimensions 6 cm in length, 4 cm in width, and 3 cm in height, the calculation is:

V = 6 cm x 4 cm x 3 cm = 72 cm³.

This provides the volume of the prism, which is the space contained within it. This value is important for determining how much material is needed to build the prism or the capacity it can hold if used as a container.

Explanation

To calculate the volume of a rectangular prism, multiply its length, width, and height together using the formula V = l x w x h, where l is the length, w is the width, and h is the height. For a prism with dimensions 6 cm in length, 4 cm in width, and 3 cm in height, the calculation is:

V = 6 cm x 4 cm x 3 cm = 72 cm³.

This provides the volume of the prism, which is the space contained within it. This value is important for determining how much material is needed to build the prism or the capacity it can hold if used as a container.

3. What is the volume of a cylinder with radius 3 cm and height 4 cm?

113.04 cm³

36 cm³

452.16 cm³

226.08 cm³

To find the volume of a cylinder, use the formula V = πr²h, where r is the radius and h is the height. Plugging in the radius of 3 cm and height of 4 cm, the calculation is:

V = π x (3 cm)² x 4 cm = π x 9 cm² x 4 cm = 36π cm³.

Using an approximation for π (about 3.14159), the volume calculation is:

36 x 3.14159 cm³ = 113.04 cm³.

This calculation shows that the volume of the cylinder is approximately 113.04 cm³, representing the amount of space inside the cylinder. This measurement is essential for applications like calculating the capacity of containers or the amount of liquid that can be stored.

Explanation

To find the volume of a cylinder, use the formula V = πr²h, where r is the radius and h is the height. Plugging in the radius of 3 cm and height of 4 cm, the calculation is:

V = π x (3 cm)² x 4 cm = π x 9 cm² x 4 cm = 36π cm³.

Using an approximation for π (about 3.14159), the volume calculation is:

36 x 3.14159 cm³ = 113.04 cm³.

This calculation shows that the volume of the cylinder is approximately 113.04 cm³, representing the amount of space inside the cylinder. This measurement is essential for applications like calculating the capacity of containers or the amount of liquid that can be stored.

4. Calculate the surface area of a cube with side length 5 cm.

150 cm²

75 cm²

300 cm²

25 cm²

To find the surface area of a cube, you multiply the area of one face by six because a cube has six identical square faces. The area of one face is given by the square of the side length, so with a side length of 5 cm, the area of one face is:

Area of one face = 5 cm x 5 cm = 25 cm².

To get the total surface area, multiply this by six:

Total surface area = 25 cm² x 6 = 150 cm².

This calculation represents the total area of all the external surfaces of the cube, which is crucial for tasks such as painting or covering the cube where the entire external surface needs to be considered.

Explanation

To find the surface area of a cube, you multiply the area of one face by six because a cube has six identical square faces. The area of one face is given by the square of the side length, so with a side length of 5 cm, the area of one face is:

Area of one face = 5 cm x 5 cm = 25 cm².

To get the total surface area, multiply this by six:

Total surface area = 25 cm² x 6 = 150 cm².

This calculation represents the total area of all the external surfaces of the cube, which is crucial for tasks such as painting or covering the cube where the entire external surface needs to be considered.

5. Find the surface area of a cylinder with radius 2 cm and height 7 cm.

113.04 cm²

56.52 cm²

452.16 cm²

226.08 cm²

To find the surface area of a cylinder, you can apply the formula A = 2 x pi x r (h + r), where r is the radius and h is the height. For a cylinder with a radius of 2 cm and a height of 7 cm, the formula works out as follows:

A = 2 x pi x 2 cm (7 cm + 2 cm) = 2 x pi x 2 cm x 9 cm = 36 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation becomes:

36 x 3.14159 cm^2 = 113.04 cm^2.

This result, 113.04 cm^2, accounts for the area of both the circular top and bottom as well as the lateral surface of the cylinder. This total surface area is crucial for tasks like material estimation for construction or manufacturing purposes involving cylindrical shapes.

Explanation

To find the surface area of a cylinder, you can apply the formula A = 2 x pi x r (h + r), where r is the radius and h is the height. For a cylinder with a radius of 2 cm and a height of 7 cm, the formula works out as follows:

A = 2 x pi x 2 cm (7 cm + 2 cm) = 2 x pi x 2 cm x 9 cm = 36 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation becomes:

36 x 3.14159 cm^2 = 113.04 cm^2.

This result, 113.04 cm^2, accounts for the area of both the circular top and bottom as well as the lateral surface of the cylinder. This total surface area is crucial for tasks like material estimation for construction or manufacturing purposes involving cylindrical shapes.

6. Calculate the volume of a cone with radius 4 cm and height 9 cm.

150.72 cm³

75.36 cm³

301.44 cm³

603 cm³

To calculate the volume of a cone, the formula V = (1/3) x pi x r^2 x h is used, where r is the radius and h is the height. For a cone with a radius of 4 cm and a height of 9 cm, the formula simplifies to:

V = (1/3) x pi x (4 cm)^2 x 9 cm = (1/3) x pi x 16 cm^2 x 9 cm = (1/3) x 144 pi cm^3 = 48 pi cm^3.

Using an approximation for pi (about 3.14159), the volume calculation is:

48 x 3.14159 cm^3 = 150.72 cm^3.

This calculation provides the volume of the cone, which is essential for understanding the space inside the cone, useful for tasks such as filling the cone with materials or analyzing its capacity in practical applications.

Explanation

To calculate the volume of a cone, the formula V = (1/3) x pi x r^2 x h is used, where r is the radius and h is the height. For a cone with a radius of 4 cm and a height of 9 cm, the formula simplifies to:

V = (1/3) x pi x (4 cm)^2 x 9 cm = (1/3) x pi x 16 cm^2 x 9 cm = (1/3) x 144 pi cm^3 = 48 pi cm^3.

Using an approximation for pi (about 3.14159), the volume calculation is:

48 x 3.14159 cm^3 = 150.72 cm^3.

This calculation provides the volume of the cone, which is essential for understanding the space inside the cone, useful for tasks such as filling the cone with materials or analyzing its capacity in practical applications.

7. Calculate the surface area of a sphere with radius 4 cm.

201.06 cm²

100.53 cm²

50.27 cm²

804.24 cm²

To calculate the surface area of a sphere, the formula used is 4 x pi x r^2, where r is the radius. For a sphere with a radius of 4 cm, the calculation proceeds as:

4 x pi x (4 cm)^2 = 4 x pi x 16 cm^2 = 64 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation becomes:

64 x 3.14159 cm^2 = 201.06 cm^2.

This value represents the total area covered by the sphere's surface. Knowing the surface area is crucial in contexts where the sphere needs to be covered or coated, as it determines the amount of material needed.

Explanation

To calculate the surface area of a sphere, the formula used is 4 x pi x r^2, where r is the radius. For a sphere with a radius of 4 cm, the calculation proceeds as:

4 x pi x (4 cm)^2 = 4 x pi x 16 cm^2 = 64 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation becomes:

64 x 3.14159 cm^2 = 201.06 cm^2.

This value represents the total area covered by the sphere's surface. Knowing the surface area is crucial in contexts where the sphere needs to be covered or coated, as it determines the amount of material needed.

8. Find the surface area of a cone with radius 5 cm and slant height 7 cm.

188.5 cm²

75.4 cm²

377 cm²

150.8 cm²

To find the surface area of a cone, use the formula A = pi x r (r + s), where r is the radius and s is the slant height. For a cone with a radius of 5 cm and a slant height of 7 cm, apply the formula:

A = pi x 5 cm (5 cm + 7 cm) = pi x 5 cm x 12 cm = 60 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation is:

60 x 3.14159 cm^2 = 188.5 cm^2.

This calculation determines the total area needed to cover the surface of the cone, combining the base and the lateral surface area, which is essential for tasks involving material use or decoration.

Explanation

To find the surface area of a cone, use the formula A = pi x r (r + s), where r is the radius and s is the slant height. For a cone with a radius of 5 cm and a slant height of 7 cm, apply the formula:

A = pi x 5 cm (5 cm + 7 cm) = pi x 5 cm x 12 cm = 60 pi cm^2.

Using an approximation for pi (about 3.14159), the surface area calculation is:

60 x 3.14159 cm^2 = 188.5 cm^2.

This calculation determines the total area needed to cover the surface of the cone, combining the base and the lateral surface area, which is essential for tasks involving material use or decoration.

9. What is the volume of a sphere with radius 6 cm?

904.78 cm³

452.39 cm³

301.59 cm³

1809.56 cm³

To calculate the volume of a sphere, use the formula V = (4/3) x pi x r^3, where r is the radius. Plugging in a radius of 6 cm, the calculation goes as follows:

V = (4/3) x pi x (6 cm)^3 = (4/3) x pi x 216 cm^3 = 288 pi cm^3.

Using an approximation for pi (about 3.14159), the volume calculation becomes:

288 x 3.14159 cm^3 = 904.78 cm^3.

This value, 904.78 cm^3, indicates the total volume inside the sphere. This measurement is crucial for applications involving the filling or manufacturing of spherical objects where internal capacity needs to be known.

Explanation

To calculate the volume of a sphere, use the formula V = (4/3) x pi x r^3, where r is the radius. Plugging in a radius of 6 cm, the calculation goes as follows:

V = (4/3) x pi x (6 cm)^3 = (4/3) x pi x 216 cm^3 = 288 pi cm^3.

Using an approximation for pi (about 3.14159), the volume calculation becomes:

288 x 3.14159 cm^3 = 904.78 cm^3.

This value, 904.78 cm^3, indicates the total volume inside the sphere. This measurement is crucial for applications involving the filling or manufacturing of spherical objects where internal capacity needs to be known.

10. What is the surface area of a rectangular prism with length 8 cm, width 5 cm, and height 2 cm?

132 cm²

58 cm²

232 cm²

174 cm²

Given dimensions:

Length (l) = 8 cm

Width (w) = 5 cm

Height (h) = 2 cm

Surface Area Formula:

Surface Area = 2 × (lw + lh + wh)

Calculate each term:

lw = 8 × 5 = 40

lh = 8 × 2 = 16

wh = 5 × 2 = 10

Sum = 40 + 16 + 10 = 66

Surface Area = 2 × 66 = 132 cm²

The surface area of the rectangular prism is 132 square centimeters.

Explanation

Given dimensions:

Length (l) = 8 cm

Width (w) = 5 cm

Height (h) = 2 cm

Surface Area Formula:

Surface Area = 2 × (lw + lh + wh)