Maths-
General
Easy

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?

hintHint:

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 l and b width  and height of the cylinder be h ,   is l cross times b cross times h , (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,
    l cross times b cross times h equals 5 cross times 4 cross times 15 equals 300 text  cubic  end text cm
    Step 2 of 3:
    We know that, if the radius of a cylinder is r and height be h , then the volume is pi r squared h .
    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,
    pi r squared h equals 22 over 7 cross times open parentheses 7 over 2 close parentheses squared cross times 10 equals 22 over 7 cross times 7 over 2 cross times 7 over 2 cross times 10 equals 385 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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