Question

lani is making a cake in the shape of a cone. to make the cake, she uses a cone shape mold. the mold has a diameter of 10 inches and a height of 12 inches. what is the volume of the cake? use 3.14 for pi. round to the nearest tenth, if necessary.

125.6 in³

314 in³

942 in³

1256 in³

Explanation:

Step1: Find the radius

The diameter is 10 inches, so the radius \( r = \frac{10}{2}=5 \) inches.

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by \( V=\frac{1}{3}\pi r^{2}h \), where \( \pi = 3.14 \), \( r = 5 \) inches, and \( h = 12 \) inches.

Step3: Substitute the values into the formula

\( V=\frac{1}{3}\times3.14\times5^{2}\times12 \)
First, calculate \( 5^{2}=25 \). Then, \( \frac{1}{3}\times12 = 4 \). So the formula becomes \( V = 3.14\times25\times4 \).
\( 25\times4 = 100 \), then \( 3.14\times100=314 \) cubic inches.

Answer:

314 in³ (corresponding to the option "314 in³")