Question

The ratio of the corresponding linear measures of two similar waffle cones is 3 to 4. The smaller cone has a volume of about 18 cubic inches. Find the volume of the larger cone. Round your answer to the nearest tenth.

Answer 1

Step 1: Since , Solids are in similar shape

$\frac{\mathrm{Volume}\mathrm{of}\mathrm{smaller}\mathrm{waffle}\mathrm{cone}}{\mathrm{Volume}\mathrm{of}\mathrm{larger}\mathrm{waffle}\mathrm{cone}}={(\mathrm{Ratio}\mathrm{of}\mathrm{corresponding}\mathrm{measures})}^3$

Step 2:

$$\begin{gathered} \frac{18}{\mathrm{V}}={\left(\frac{3}{4}\right)}^3 \\ \frac{18}{\mathrm{V}}=\frac{27}{64} \\ 18*64=27*\mathrm{V} \\ \mathrm{V}=\frac{18*64}{27} \\ \mathrm{V}=42.67 \end{gathered}$$

Final Answer: The volume of larger cone is about 42.7 cubic inches