A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time. Both containers have the same volume. (i) Tin A has a radius of 3 cm and a height of 10.6 cm. Find the volume of tin A. Give your answer correct to the nearest whole number. (ii) Carton B has a square base of length 5 cm. Use the answer you got in (i) above to find the height of carton B. (iii) Which one of the above containers do you think the company might choose? Give a reason for your answer.

Junior Cycle Mathematics Area & Volume: A food production company has to

A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time - Junior Cycle Mathematics - Question 2 - 2014

Question 2

A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time. Both co... show full transcript

Worked Solution & Example Answer:A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time - Junior Cycle Mathematics - Question 2 - 2014

Step 1

Find the volume of tin A.

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Answer

To find the volume of a cylinder, we use the formula:

$V = \\pi r^2 h$

Where:

$r = 3$ cm (radius)
$h = 10.6$ cm (height)

Now substituting in the values:

$V = \\pi (3^2)(10.6) = \\pi (9)(10.6) = \\pi (95.4)$

Calculating the value:

$V \approx 299.8 \\text{ cm}^3$

Rounding to the nearest whole number, the volume of tin A is 300 cm³.

Step 2

Use the answer you got in (i) above to find the height of carton B.

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Answer

The volume of carton B can be expressed as:

$V_B = ext{base area} \times ext{height} = (5 \times 5) \times h$

Given that the volume of carton B is equal to that of tin A:

$25h = 300 \\Rightarrow h = \frac{300}{25} = 12 \\text{ cm}$

Thus, the height of carton B is 12 cm.

Step 3

Which one of the above containers do you think the company might choose? Give a reason for your answer.

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Answer

I think the company might choose the carton B. They can potentially use a smaller packing case to hold several cartons as compared with an equal number of tins of the same volume. Alternatively, they might choose the tin, as it may suit the shape of the product better.

A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time - Junior Cycle Mathematics - Question 2 - 2014

Worked Solution & Example Answer:A food production company has to decide between a closed cylindrical tin A or a rectangular carton B to hold a product they are marketing for the first time - Junior Cycle Mathematics - Question 2 - 2014

Find the volume of tin A.

Use the answer you got in (i) above to find the height of carton B.

Which one of the above containers do you think the company might choose? Give a reason for your answer.

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