Question

question
find the volume of a right circular cone that has a height of 19.4 cm and a base with a diameter of 9.9 cm. round your answer to the nearest tenth of a cubic centimeter.
answer attempt 2 out of 2
cm³ submit answer

Explanation:

Step1: Find the radius of the base

The diameter of the base is 9.9 cm, so the radius \( r \) is half of the diameter.
\( r=\frac{9.9}{2}=4.95 \) cm.

Step2: Recall the formula for the volume of a cone

The volume \( V \) of a right circular cone is given by the formula \( V = \frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know \( r = 4.95 \) cm and \( h=19.4 \) cm. Substituting these values into the formula:
\( V=\frac{1}{3}\times\pi\times(4.95)^{2}\times19.4 \)

First, calculate \( (4.95)^{2}=4.95\times4.95 = 24.5025 \)

Then, multiply by \( 19.4 \): \( 24.5025\times19.4 = 24.5025\times(20 - 0.6)=24.5025\times20-24.5025\times0.6 = 490.05- 14.7015=475.3485\)

Then, multiply by \( \frac{1}{3}\pi \): \( V=\frac{1}{3}\times\pi\times475.3485\approx\frac{1}{3}\times3.14159\times475.3485\)

\( \frac{3.14159\times475.3485}{3}\approx\frac{1493.03}{3}\approx497.7\) (rounded to the nearest tenth)

Answer:

\( 497.7 \)