Question

Two cones are similar. The surface area of the larger cone is 65π square inches. The surface area of the smaller cone is 41.6π square inches. The radius of the smaller cone is 6.4 inches. What is the radius of the larger cone?
8 inches
10 inches
11.52 inches
14.4 inches

Answer 1

8 inches hope it helps

Answer 2

Step $1$

Find the scale factor

we know that

$surface\ area\ of\ the\ larger\ cone=(scale\ factor^{2})* surface\ area\ of\ the\ smaller\ cone$

$(scale\ factor^{2})=surface\ area\ of\ the\ larger\ cone/ surface\ area\ of\ the\ smaller\ cone$

in this problem we have

$surface\ area\ of\ the\ larger\ cone=65\pi\ in^{2} \\surface\ area\ of\ the\ smaller\ cone=41.6\pi\ in^{2}$

Substitute the values

$(scale\ factor^{2})=\frac{65\pi }{41.6\pi } =1.5625\\ scale\ factor=1.25$

Step $2$

Find the radius of the larger cone

we know that

$the\ radius\ of\ the\ larger\ cone=(scale\ factor)* the\ radius\ of\ the\ smaller\ cone$

in this problem we have

$the\ radius\ of\ the\ smaller\ cone=6.4\ in$

substitute

$the\ radius\ of\ the\ larger\ cone=1.25* 6.4=8\ in$

therefore

the answer is

the radius of the larger cone is $8\ in$