Answered

Solids H and Q are similar. H has 8.5 times the surface area as Q. Q has a
height of 5 in. What is the height of H? Round your answer to two decimal
places if necessary.
Show your work here
O-17.58
O 17.58
O 14.58
O 15.58

Verified Answer :

GinnyAnswer

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 \(\( h_H \)\) be the height of solid H, and \(\( h_Q \)\) be the height of solid Q.
- The ratio of the heights will be the square root of the ratio of the surface areas.
\(\[ \frac{h_H}{h_Q} = \sqrt{\text{ratio of surface areas}} \]\)
- Plugging in the given values:
\(\[ \frac{h_H}{5} = \sqrt{8.5} \]\)

4. Calculate the square root:
\(\[ \sqrt{8.5} \approx 2.915 \]\)

5. Determine the height of H:
\(\[ h_H = 2.915 \times 5 = 14.575 \]\)

6. Round to two decimal places:
\(\[ h_H \approx 14.58 \text{ inches} \]\)

Thus, the height of solid H is approximately 14.58 inches.

The correct answer is 14.58.

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