Question

which cone is similar to a right cone with a height of 3 ft and a base with a diameter of 5 ft?

Explanation:

Step1: Find the ratio of height to diameter for the original cone.

The original cone has height \( h_1 = 3 \) ft and diameter \( d_1 = 5 \) ft. So the ratio is \( \frac{h_1}{d_1}=\frac{3}{5} \).

Step2: Calculate the ratio for each option.

• Option 1: Height \( h = 9 \) ft, diameter \( d = 25 \) ft. Ratio: \( \frac{9}{25}

eq\frac{3}{5} \).

• Option 2: Height \( h = 5 \) ft, diameter \( d = 7 \) ft. Ratio: \( \frac{5}{7}

eq\frac{3}{5} \).

• Option 3: Height \( h = 10 \) ft, diameter \( d = 6 \) ft. Ratio: \( \frac{10}{6}=\frac{5}{3}

eq\frac{3}{5} \).

• Option 4: Height \( h = 12 \) ft, diameter \( d = 20 \) ft. Ratio: \( \frac{12}{20}=\frac{3}{5} \), which matches the original ratio.

Answer:

The cone with height 12 ft and diameter 20 ft (the fourth cone).