Alright, let's work through this step-by-step to find the height of Solid H.
1. Understand the relationship between the surface areas and heights of similar solids:
- Since solids H and Q are similar, the ratio of their surface areas is the square of the ratio of their corresponding linear dimensions (such as height).
2. Given data:
- The surface area of H is 8.5 times the surface area of Q.
- The height of Q is 5 inches.
3. Establish the ratio of the heights:
- Let [tex]\( h_H \)[/tex] be the height of solid H, and [tex]\( h_Q \)[/tex] be the height of solid Q.
- The ratio of the heights will be the square root of the ratio of the surface areas.
[tex]\[
\frac{h_H}{h_Q} = \sqrt{\text{ratio of surface areas}}
\][/tex]
- Plugging in the given values:
[tex]\[
\frac{h_H}{5} = \sqrt{8.5}
\][/tex]
4. Calculate the square root:
[tex]\[
\sqrt{8.5} \approx 2.915
\][/tex]
5. Determine the height of H:
[tex]\[
h_H = 2.915 \times 5 = 14.575
\][/tex]
6. Round to two decimal places:
[tex]\[
h_H \approx 14.58 \text{ inches}
\][/tex]
Thus, the height of solid H is approximately 14.58 inches.
The correct answer is 14.58.
