Question

The ratio of corresponding dimensions of two similar solids is 1 half. The surface area of the first solid is 330 m2. Its volume is 624 m3. Find the surface area and volume of the second solid. Round each answer to the nearest tenth, if necessary.

Answer 1

Part 1) The surface area of the second solid is
`82.5\ m^(2)`

Part 2) The volume of the second solid is
`78\ m^(3)`

Explanation:

In this problem we have

`scale\ factor=(1)/(2)`

Part 1)

we know that

The ratio of the surface areas of two similar solids is equal to the scale factor squared

Let

x------> the surface area of the second solid (reduced solid)

y------> the surface area of the first solid (original solid)

z-----> the scale factor

`z^(2)=(x)/(y)`

we have

`z=(1)/(2)`

`y=330\ m^(2)`

substitute and solve for x

`((1)/(2))^(2)=(x)/(330)`

`x=(1)/(4)*330=82.5\ m^(2)`

Part 2)

we know that

The ratio of the volumes of two similar solids is equal to the scale factor elevated to the cube

Let

x------> the volume of the second solid (reduced solid)

y------> the volume of the first solid (original solid)

z-----> the scale factor

`z^(3)=(x)/(y)`

we have

`z=(1)/(2)`

`y=624\ m^(3)`

substitute and solve for x

`((1)/(2))^(3)=(x)/(624)`

`x=(1)/(8)*624=78\ m^(3)`