Exercise 1

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

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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 per square meter.</span>   <span class="actividades_r"><span class="numero_v">1 </span>How much will it cost to paint the interior surfaces of the pool?</span> <span class="numero_v">2</span>How many liters of water will be needed to fill it?   <h2>Exercise 3</h2><span class="actividades_g">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?</span>        <h2>Exercise 4</h2><span class="actividades_g">Calculate the suface area of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/regular-tetrahedron.html" style="text-decoration:underline;">regular tetrahedron</a>,  octahedron and  icosahedron, each with an edge of 5 cm.</span> <h2>Exercise 5</h2> <span class="actividades_g">Calculate the height of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/prisms.html" style="text-decoration:underline;">prism</a> whose base area is 12  dm² and whose capacity is 48 liters.</span>        <h2>Exercise 6</h2><span class="actividades_g">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.</span>        <h2>Exercise 7</h2>The height of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/cylinder.html" style="text-decoration:underline;">cylinder</a> is the same length as the <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/circumference.html" style="text-decoration:underline;">circumference</a> of its base. Its measured height is 125.66 cm. Calculate the surface area and volume of the cylinder: <h2>Exercise 8</h2><span class="actividades_g">Four <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/regular-hexahedron-or-cube.html" style="text-decoration:underline;">cubes</a> 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?</span> <h2>Exercise 9</h2><span class="actividades_g">The dome of a cathedral has a semispherical form with a radius of 50 m. If the restoration costs300 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 centimeters) of a prism that is 5 m long, 40 cm wide and 2,500 mm high.

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 per square meter.   <span class="numero_v">1 </span>How much will it cost to paint the interior surfaces of the pool? <span class="numero_v">2 </span> How many liters of water will be needed to fill it? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/66-15615376524475-4704.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/67_1-15615376525706-8557.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/67_2-15615376527374-8168.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/67_3-15615376528332-2807.gif"   >                  <h2>Solution of exercise 3</h2>    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? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/77-15615376530007-544.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_1-15615376531241-5656.gif"   >                  <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_2-15615376532037-2505.gif"   >                 <span class="ar" style="margin-left:45%;"><img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_3-15615376532861-7361.gif"   ></span>                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_4-15615376534254-1593.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_5-15615376535101-8654.gif"   >                 <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/78_6-15615376536331-6863.gif"   >                  <h2>Solution of exercise 4</h2>   Calculate the suface area of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/regular-tetrahedron.html" title="tetrahedron" style="text-decoration:underline;">regular tetrahedron</a>,  octahedron and  icosahedron, each with an edge of 5 cm. <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/79_1-15615376537115-9795.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/79_2-15615376537849-9158.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/79_3-15615376539103-2236.gif"   >                          <h2>Solution of exercise 5</h2>   Calculate the height of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/prisms.html" title="prism" style="text-decoration:underline;">prism</a> whose base area is 12  dm² and whose capacity is 48 liters. <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/76_1-15615376540437-5295.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/76_2-15615376541086-1986.gif"   >                                                   <h2>Solution of exercise 6</h2>   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. <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/70-15615376541925-2009.gif"   >                       <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/71_1-15615376542973-1356.gif"   >                       <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/71_2-15615376544083-2776.gif"   >                                                                  <h2>Solution of exercise 7</h2>   The height of a <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/cylinder.html" title="cylinder" style="text-decoration:underline;">cylinder</a> is the same length as the <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/plane/circumference.html" title="circumference" style="text-decoration:underline;">circumference</a> of its base. Its measured height is 125.66 cm. Calculate the surface area and volume of the cylinder: <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/81_1-15615376545016-3308.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/81_2-15615376546416-9348.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/81_3-15615376548631-4779.gif"   >                          <h2>Solution of exercise 8</h2>   Four <a href="https://www.superprof.co.uk/resources/academic/maths/geometry/solid/regular-hexahedron-or-cube.html" title="cubes" style="text-decoration:underline;">cubes</a> 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? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/85_1-15615376550126-622.gif"   >                         <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/85_2-15615376551092-7572.gif"   >      <h2>Solution of exercise 9</h2>   The dome of a cathedral has a hemispherical form with a radius of 50 m. If the restoration costs300 per m², what is the total cost of the restoration?

15,707.96 · 300 = $4,712,388.98

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?

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?

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?

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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.

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