Respuesta :
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
[tex]V = a \times b \times c \: \rm unit^3[/tex]
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,
[tex]60 \: \rm cm^3 = 5\times b\times c \\\\b\times c = \dfrac{60}{5} = 12[/tex]
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
[tex]15 \times 3 \times b \times 3 \times c = 135 \times b\times c = 135 \times 12 = 1620 \: \rm cm^3[/tex]
Thus,
The volume of the larger rectangular prism is given as: Option C: 1620 cm³
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