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Exercise 1

Calculate the volume (in cubic centimetres) of a prism that is 5 m long, 400 cm wide and 2500 mm high.

Exercise 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 dollars per square meter.

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

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

Exercise 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?

Exercise 4

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

Exercise 5

Calculate the height of a prism whose base area is 12 dm² and whose capacity is 48 litres.

Exercise 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.

Exercise 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:

Exercise 8

Four cubes of ice with an edge of 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?

Exercise 9

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

Exercise 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?

Exercise 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?

Exercise 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?

Exercise 13

A 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?

 

Solution of exercise 1

Calculate the volume (in cubic centimetres) of a prism that is 5 m long, 400 cm wide and 2,500 mm high.

 

Since

 

Solution of exercise 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 dollars per square meter.

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

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

 

dollars

 

Solution of exercise 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?

 

No. of boxes =

 

Solution of exercise 4

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

 

Solution of exercise 5

Calculate the height of a prism whose base area is 12 dm² and whose capacity is 48 litres.

 

Solution of exercise 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.

 

 

Solution of exercise 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:

 

Solution of exercise 8

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

 

Solution of exercise 9

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

dollars

 

Solution of exercise 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?

 

Since

No. of tiles =

 

Solution of exercise 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?

Mass of the container =

 

Solution of exercise 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?

 

 

Solution of exercise 13

A 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?

Yes, the amount of water can easily fit inside of the sphere.

 

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Emma

Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.