Step-by-step explanation:
the volume of a figure bases always on a calculation that multiplies 3 dimensions.
while a surface area bases always on a calculation that multiplies 2 dimensions.
since the figures are similar, that means that all dimensions or side lengths of one figure correlate to the corresponding dimensions or side lengths of the other figure via the same scale factor f.
and that means that
large side length = small side length × f.
and that means that f has to be multiplied in 3 times for the volume and 2 times for the surface area (once for every dimension).
so,
large volume = small volume × f × f × f =
= small volume × f³
1536 = 648 × f³
f³ = 1536/648 = 64/27
f = 4/3
and
large surface = small surface × f×f =
= small surface × f²
small surface = large surface / f² = 864 / 16/9 =
= 864 × 9/16 = 54 × 9 = 486 m²
