# Volume Word Problems

### Solutions

1Calculate the volume (in cubic centimeters) of a prism that is 5 m long, 40 cm wide and 2500 mm high.

2A swimming pool is 8 m long, 6 m wide and 1.5 m deep. The water resistant paint needed for the pool costs $6 per square meter.

1 How much will it cost to paint the interior surfaces of the pool?

2How many liters of water will be needed to fill it?

3A moving company is trying to store boxes in a storage room with a length of 5 m, width of 3 m and height of 2 m. How many boxes can fit in this space if each is 10 cm long, 6 cm wide and 4 cm high?

4Calculate the suface area of a regular tetrahedron, octahedron and icosahedron, each with an edge of 5 cm.

5 Calculate the height of a prism whose base area is 12 dm^{2} and whose capacity is 48 liters.

6Calculate the quantity of sheet metal that would be needed to make 10 cylindrical canisters with a diameter of 10 cm and a height of 20 cm.

7The height of a cylinder is the same length as the circumference of its base. Its measured height is 125.66 cm. Calculate the surface area and volume of the cylinder:

8Four cubes of ice with an edge 4 cm each are left to melt in a cylinderical glass with a radius of 6 cm. How high will the water rise when they have melted?

9The dome of a cathedral has a semispherical form with a radius of 50 m. If the restoration costs $300 per m², what is the total cost of the restoration?

10How many square tiles (20 cm x 20 cm) are needed to coat the sides and base of a pool which is 10 m long, 6 meters wide and 3 m deep?

11A cylindrical container with a radius of 10 cm and a height of 5 cm is filled with water. If the total mass of the filled container is 2 kg, what is the mass of the empty container?

12For a party, Louis has made about 10 conical hats out of cardboard. How much cardboard was used in total if each cap has a radius of 15 cm and a slant height of 25 cm?

13A cube with an edge of 20 cm is filled with water. Would this amount of water fit in a sphere with a 20 cm radius?

## 1

Calculate the volume (in cubic centimeters) of a prism that is 5 m long, 40 cm wide and 2,500 mm high.

## 2

A swimming pool is 8 m long, 6 m wide and 1.5 m deep. The water resistant paint needed for the pool costs $6 per square meter.

1 How much will it cost to paint the interior surfaces of the pool?

2 How many liters of water will be needed to fill it?

## 3

A moving company is trying to store boxes in a storage room with a length of 5 m, width of 3 m and height of 2 m. How many boxes can fit in this space if each is 10 cm long, 6 cm wide and 4 cm high?

## 4

Calculate the suface area of a regular tetrahedron, octahedron and icosahedron, each with an edge of 5 cm.

## 6

Calculate the quantity of sheet metal that would be needed to make 10 cylindrical canisters with a diameter of 10 cm and a height of 20 cm.

## 7

The height of a cylinder is the same length as the circumference of its base. Its measured height is 125.66 cm. Calculate the surface area and volume of the cylinder:

## 8

Four cubes of ice with an edge 4 cm each are left to melt in a cylinderical glass with a radius of 6 cm. How high will the water rise when they have melted?

## 9

The dome of a cathedral has a hemispherical form with a radius of 50 m. If the restoration costs $300 per m², what is the total cost of the restoration?

15,707.96 · 300 = **$4,712,388.98**

## 10

How many square tiles (20 cm x 20 cm) are needed to coat the sides and base of a pool which is 10 m long, 6 meters wide and 3 m deep?

## 11

A cylindrical container with a radius of 10 cm and a height of 5 cm is filled with water. If the total mass of the filled container is 2 kg, what is the mass of the empty container?

## 12

For a party, Louis has made about 10 conical hats out of cardboard. How much cardboard was used in total if each cap has a radius of 15 cm and a slant height of 25 cm?