Question

Two similar solids have base areas of 47 cm² and 199 cm², as shown below.

The volume of the smaller solid is 350 cm³.
COMPLETION
50%
Calculate the volume of the larger solid correct to the nearest integer.
(4 marks)

Answer 1

Check the picture below.

so hmmm let's use the ratio for the areas to get the ratio of the sides, and from there, we'll get to the ratio of the volumes.

`\stackrel{ \textit{Areas' ratio} }{\sqrt{\cfrac{s^2}{s^2}}}=\cfrac{s}{s}\implies \sqrt{\cfrac{47}{199}}=\cfrac{s}{s}\implies \cfrac{√(47)}{√(199)}=\cfrac{s}{s} \\\\[-0.35em] ~\dotfill`

`\stackrel{ \textit{Volumes' ratio} }{\sqrt[3]{\cfrac{s^3}{s^3}}}=\cfrac{s}{s}\implies \stackrel{\textit{substituting from above}}{\sqrt[3]{\cfrac{s^3}{s^3}}=\cfrac{√(47)}{√(199)}}\implies \sqrt[3]{\cfrac{350}{V}}=\cfrac{√(47)}{√(199)} \\\\\\ \cfrac{350}{V}=\left( \cfrac{√(47)}{√(199)} \right)^3\implies \cfrac{350}{V}=\cfrac{√(47^3)}{√(199^3)}\implies (350)(√(199^3))=V√(47^3) \\\\\\ \cfrac{(350)(√(199^3))}{√(47^3)}=V\implies \boxed{3049\approx V}`