Question

the height of the cone in figure 2 is centimeters. figure 1 is similar to figure 2. type the correct answer in the box.

Explanation:

Step1: Set up proportion for similar - cones

Since the two cones are similar, the ratios of their corresponding linear dimensions (radius and height) are equal. Let the height of the cone in figure 2 be \(h\). The ratio of the radii of the two cones is \(\frac{8}{3}\), and the ratio of the heights should be the same. The height of the cone in figure 1 is 12 cm. So, we have the proportion \(\frac{8}{3}=\frac{12}{h}\).

Step2: Cross - multiply to solve for \(h\)

Cross - multiplying the proportion \(\frac{8}{3}=\frac{12}{h}\) gives us \(8h = 3\times12\).

Step3: Simplify the right - hand side

\(3\times12 = 36\), so the equation becomes \(8h=36\).

Step4: Solve for \(h\)

Dividing both sides of the equation \(8h = 36\) by 8, we get \(h=\frac{36}{8}=\frac{9}{2}=4.5\) cm.

Answer:

4.5