Question
A soft drink is available in two packs. i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Hint:
The volume of a cylinder with any kind of base (rectangular or circular) is the area of its base multiplied by the height of the cylinder, i.e., if the height of a cylinder is h , then its volume is given by, (area x h) cubic units.
The correct answer is: The plastic cylinder has greater capacity by 85 cm3 more than the tin can.
Explanations:
Step 1 of 3:
The volume of a cylinder, with a rectangular base of length 
and b width and height of the cylinder be h , is 
, (since the area of a rectangle is length x width).
So, the capacity (or volume) of the tin can with a rectangular base of length ( l) 5 cm and width (b) 4 cm, having a height (h) of 15 cm, is given by,
Step 2 of 3:
We know that, if the radius of a cylinder is r and height be h , then the volume is 
.
So, the capacity of the plastic cylinder with circular base of diameter 7 cm (so radius (r) is 7/2 cm) and height (h) 10 cm, is given by,
cm3
Step 3 of 3:
The tin can have a capacity of 300 cm3 and the plastic cylinder has of 385 cm3
So, clearly 385 > 300, hence the plastic cylinder has greater capacity, by (385 – 300) = 85 cm3 more.
Final Answer:
The plastic cylinder has greater capacity by 85 cm3 more than the tin can.
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