Question

A prism has total surface area of 360 m2 and volume of 60 m3.

If the length, width, and height are reduced to half their original sizes, what will be the following?

(a) the new surface area(5 pts)

(b) the new volume(5 pts)


If the length, width, and height of the original are increased to triple their original sizes, what will be the following?

(c) the new surface area(5 pts)

(d) the new volume(5 pts)

Answer 1

we know that

If each dimension is scaled by a factor x, then the area of each side, and thus the surface area, is scaled by x² and the volume is scaled by x³.

Thus,
Part a) if the length, width, and height are reduced to half their original sizes, the area of each side is scaled by a factor of
(1/2)²------> 1/4
and
the volume is scaled by a factor of
(1/2)³-----> 1/8.

Thus,
if the initial surface area is 360 m²,
the final surface area is (1/4)(360 m²) = 90 m².

If the initial volume is 60 m³,
then
the final volume is (1/8)(60 m³) = 7.5 m³.

Part B_ If the length, width, and height are tripled, the area of each side is scaled by a factor of
(3)²-----> 9
and
the volume is scaled by a factor of
(3)³-------> 27.

Thus,
if the initial surface area is 360 m²,
the final surface area is (9)(360 m^2) = 3240 m².

If the initial volume is 60 m³,
then
the final volume is (27)(60 m^3) = 1620 m³.