Question

The two rectangular prisms are similar.

What is the volume of the larger rectangular prism?




240 cm³

540 cm³

1620 cm³

3240 cm³

Answer 1

We have the volume of the original prism is:
V = (l) * (w) * (t)
where,
l = long,
w: width
t: depth
For this case we can see that the original rectangular prism is dilated by a factor of 3
V = (3l) * (3w) * (3t)
V = (l) * (w) * (t) * (3) * (3) * (3)
V = (60) * (27)
V = 1620 cm ^ 3
answer
the volume of the larger rectangular prism is 1620 cm ^ 3

Answer 2

If two solids are similar the ratio of the corresponding sides is called the linear scale factor while the ratio of the areas is called the area scale factor and the ratio of their volumes is the volume scale factor.
v.s.f = (l.s.f)³
in this case, the l.s.f = 5/15 = 1/3
therefore, the V.S.F = (1/3)³ = 1/27
Thus the volume of the larger prism = 60 ×27
= 1620 cm³