Question

The surface areas of two similar solids are 312 ft2 and 1,198 ft2. The volume of the smaller solid is 239 ft3. What is the volume of the larger solid? 1,798 ft3

Answer 1

1,798 ft3

Explanation:

Answer 2

The volume of the larger solid is
`1,798\ ft^(3)`

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar , then the ratio of its surface areas is equal to the scale factor squared

so

Let

z-------> the scale factor

x-------------> surface area larger solid

y-------------> surface area smaller solid

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

substitute

`z^(2) =(1,198)/(312)`

`z=\sqrt{(1,198)/(312)}` ----> scale factor

step 2

Find the volume of the larger solid

we know that

If two figures are similar , then the ratio of its volumes is equal to the scale factor elevated to the cube

so

Let

z-------> the scale factor

x-------------> volume of the larger solid

y-------------> volume of the smaller solid

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

we have

`z=\sqrt{(1,198)/(312)}`

`y=239\ ft^(3)`

substitute the values

`(\sqrt{(1,198)/(312)}^(3))=(x)/(239)`

`x=239*(\sqrt{(1,198)/(312)}^(3))=1,798\ ft^(3)`