Question

The two rectangular prisms are similar. What is the volume of the larger rectangular prism? 240 cm³ 540 cm³ 1620 cm³ 3240 cm³ A smaller rectangular prism with a side length of five centimeters and volume of sixty cubic centimeters. A larger, similar rectangular prism with a side length of fifteen centimeters.

Answer 1

Volume of a figure is measure of the space it occupies. The volume of the larger rectangular prism is given as: Option C: 1620 cm³

How to calculate volume of a rectangular prism?

If a rectangular prism has dimensions a unit, b unit, and c units, then its volume is given as

$V = a \times b \times c \: \rm unit^3$

What are similar figures?

They are scaled. It means, if two figures are similar, then we can get one figure from another by multiplying some constant value(same for one pair of similar figure) to its dimensions.

For example,

if for given case, one rectangular prism has got dimensions a, b, and c centimetres, then

the second rectangular prism, which is similar, let the scale factor is 'd',t then second prism's dimensions will be a x d units, b x d units, and  c x d units.

For first prism(smaller), its one side is given to be 5 cm, let its other two sides be 'b' cm, and 'c' cm, then,

$60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12$

Now, the larger prism has 15 cm corresponding side, thus, scale factor was 3 (since 15 is 3 times 5).

Thus, its dimensions would be 15, 3 x b, 3 x c

Thus, its volume would be

$15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3$

Thus,

The volume of the larger rectangular prism is given as: Option C: 1620 cm³

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