Question

A rectangular prism aquarium holds 64 gallons of water. A similarly shaped aquarium holds 8 gallons of water. If a 1.5 ft2 cover fits on the smaller tank, what is the area of a cover that will fit on the larger tank

Answer 1

The area of a cover that will fit on the larger tank is 6 square inches

Explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its Volumes is equal to the scale factor cubed

Let

z ---> the scale factor

so

`z^3=(64)/(8)=8`

`z=2`

step 2

we know that

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

Let

z ---> the scale factor

x ---> the area of a cover that will fit on the larger tank

y ---> the area of a cover that will fit on the smaller tank

so

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

we have

`z=2\\y=1.5\ ft^2`

substitute the given values

`2^2=(x)/(1.5)`

solve for x

`x=4(1.5)=6\ ft^2`