Cement is stored in a silo in the shape of a cylinder on a cone as shown in the diagram. (a) The height of the cylinder is 7 m and the radius is 2 m. Find the volume of the cylinder. Use π = 3.142. Give your answer correct to the nearest m³. (b) The volume of the cone is 12 m³. Find the total volume of cement in the silo when it is full. Give your answer correct to the nearest m³. (c) If 1 m³ of cement weighs 2.5 tonnes, what is the total weight of the cement in the silo?

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Cement is stored in a silo in the shape of a cylinder on a cone as shown in the diagram - Junior Cycle Mathematics - Question 8 - 2013

Question 8

Cement is stored in a silo in the shape of a cylinder on a cone as shown in the diagram. (a) The height of the cylinder is 7 m and the radius is 2 m. Find the volum... show full transcript

Worked Solution & Example Answer:Cement is stored in a silo in the shape of a cylinder on a cone as shown in the diagram - Junior Cycle Mathematics - Question 8 - 2013

Step 1

Find the volume of the cylinder.

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Answer

To find the volume of the cylinder, we can use the formula: $V = ext{π} r^2 h$ where

$ext{r} = 2 ext{ m}$
$ext{h} = 7 ext{ m}$ .

Substituting the values into the formula gives:

$V = 3.142 imes 2^2 imes 7$

Calculating this yields:

$V = 3.142 imes 4 imes 7 = 3.142 imes 28 = 87.976$

Rounding to the nearest m³, the volume of the cylinder is 88 m³.

Step 2

Find the total volume of cement in the silo when it is full.

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Answer

The total volume in the silo when full is the sum of the volumes of the cylinder and the cone:

Total volume = Volume of cylinder + Volume of cone

Substituting the known values:

Total volume = $88 ext{ m}³ + 12 ext{ m}³ = 100 ext{ m}³$ .

Step 3

If 1 m³ of cement weighs 2.5 tonnes, what is the total weight of the cement in the silo?

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Answer

To find the total weight of the cement, use the formula:

Total weight = Total volume × Weight per m³

Substituting the known values:

Total weight = $100 ext{ m}³ × 2.5 ext{ tonnes/m}³ = 250 ext{ tonnes}$ .

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