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,

cm^{3}

Step 3 of 3:

The tin can have a capacity of 300 cm^{3 }and the plastic cylinder has of 385 cm^{3}

So, clearly 385 > 300, hence the plastic cylinder has greater capacity, by (385 – 300) = 85 cm^{3} more.

Final Answer:

The plastic cylinder has greater capacity by 85 cm^{3 }more than the tin can.

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