Question

The volumes of two similar solids are 729 inches3 and 125 inches3. if the surface area of the smaller solid is 74.32 inches2, what is the surface area of the larger solid? round to the nearest hundredth. 133.78 in.2 240.80 in.2 433.43 in.2 678.32 in.2

Answer 1

The answer is B. 240.80 in.^2

Answer 2

The correct answer is B. 240.80 inches²

Explanation:

The volume scale factor will be given by :

`=\frac{\text{Volume of larger solid}}{\text{Volume of smaller solid}}\\\\=(729)/(125)`

`\text{But, linear scale factor = }\text{(volume scale factor)}^{(1)/(3)}`

`\text{Thus the linear scale factor will be : }((729)/(125))^{(1)/(3)}= (9)/(5)`

Also, Area scale factor will be given by :

Area scale factor = (linear scale factor)²

`((9)/(5))^2\\\\=(81)/(25)`

Let the area of the larger solid be A

The area of the larger solid will be given by :

`(A)/(74.32)=(81)/(25)\\\\\implies A = (74.32* 81)/(25)\\\\ \implies A = 240.80`

Hence, Area of the larger solid = 240.80 inches²

Therefore, The correct answer is B. 240.80 inches²