Sofia is estimating the volume of a shed. (a) She thinks that the base of the shed is roughly a rectangle with a length of 40 m and a width of 18 m. Work out the area of this rectangle. (b) Sofia thinks that the shed is roughly in the shape of a rectangular box with a length of 40 m, a width of 18 m, and a height of 14 m. Work out the volume of this box. The diagram below shows the actual shed that Sofia is interested in. All of the measurements are in metres.

Junior Cycle Mathematics Area & Volume: Sofia is estimating the volume o

Sofia is estimating the volume of a shed - Junior Cycle Mathematics - Question 1

Question 1

Sofia is estimating the volume of a shed. (a) She thinks that the base of the shed is roughly a rectangle with a length of 40 m and a width of 18 m. Work out the ar... show full transcript

Worked Solution & Example Answer:Sofia is estimating the volume of a shed - Junior Cycle Mathematics - Question 1

Step 1

a) Work out the area of this rectangle.

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Answer

To calculate the area of a rectangle, we use the formula:

ext{Area} = ext{length} imes ext{width}

In this case, the length is 40 m and the width is 18 m, so:

ext{Area} = 40 imes 18 = 720 ext{ m}^2

Thus, the area of the rectangle is 720 m².

Step 2

b) Work out the volume of this box.

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Answer

To find the volume of a rectangular box, we use the formula:

ext{Volume} = ext{length} imes ext{width} imes ext{height}

Here, the length is 40 m, the width is 18 m, and the height is 14 m. Therefore:

ext{Volume} = 40 imes 18 imes 14

Calculating this gives:

ext{Volume} = 40 imes 18 = 720,

and then:

720 imes 14 = 10,080 ext{ m}^3

Hence, the volume of the box is 10,080 m³.

Step 3

c) Based on the diagram, what do you need to do to your answer to part (b) to get a more accurate estimate of the volume of the shed?

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Answer

To get a more accurate estimate of the volume of the shed, one must consider that the actual shape of the shed is not entirely rectangular. The shed has sloped sides, indicating a different geometry than that of the box used to estimate the volume. Therefore, instead of using the full height, we should reduce the height, or alternatively, calculate the volume of the shed based on the actual dimensions shown in the diagram.

Sofia is estimating the volume of a shed - Junior Cycle Mathematics - Question 1

Worked Solution & Example Answer:Sofia is estimating the volume of a shed - Junior Cycle Mathematics - Question 1

a) Work out the area of this rectangle.

b) Work out the volume of this box.

c) Based on the diagram, what do you need to do to your answer to part (b) to get a more accurate estimate of the volume of the shed?

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