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A can in the shape of a cylinder has a radius of 3.6 cm and a height of 10 cm - Junior Cycle Mathematics - Question 9 - 2021
Question 9
A can in the shape of a cylinder has a radius of 3.6 cm and a height of 10 cm. Work out the volume of the can. Give your answer in cm³, correct to two decimal places... show full transcript
Worked Solution & Example Answer:A can in the shape of a cylinder has a radius of 3.6 cm and a height of 10 cm - Junior Cycle Mathematics - Question 9 - 2021
Step 1
Work out the volume of the can.
Answer
To calculate the volume of a cylinder, we use the formula:
ho imes h$$ where the base area is \ $$ ext{base area} = ext{Area} = imes ext{radius}^2 imes ext{height}$$ Substituting the radius (3.6 cm) and height (10 cm), $$V = rac{22}{7} imes (3.6)^2 imes 10 = rac{22}{7} imes 12.96 imes 10 \ \approx 405.43 ext{ cm}^3$$ Thus, the volume of one can is approximately **405.43 cm³**.Step 2
Write down the height, length, and width of the box.
Answer
Given the arrangement of the cans:
- Height = 10 cm (height of one can)
- Length = 28.8 cm (already provided)
- Width = 8 cm (calculated as follows: each can has a diameter of 2 * radius = 7.2 cm, and if arranged 3 cans wide, Width = 7.2 * 3 = 21.6 cm, allowing some additional space, we can say width = 8 cm)
Step 3
Step 4
Work out the percentage of the volume of this box that is taken up by the 24 cans.
Answer
To find the percentage of volume occupied by the cans, use the formula: ext{Percentage} = rac{ ext{Volume of cans}}{ ext{Volume of box}} imes 100 Substituting the values:
ext{Approximately} = 422.8 ext{%}$$Step 5
Find the dimensions of the rectangular box required for a different arrangement of the 24 cans.
Answer
Assuming a different arrangement, let’s consider the cans could be arranged in 4 layers of 6 cans each:
- Height = 4 * 10 cm = 40 cm
- Length = 6 * 7.2 cm = 43.2 cm
- Width = 10 cm Thus, height = 40 cm, length = 43.2 cm, width = 10 cm.