What is the volume of a cone with a height of 27 cm and a radius of 13 cm? Round your answer to the nearest tenth.

1 answer

The volume \( V \) of a cone can be calculated using the formula:

\[ V = \frac{1}{3} \pi r^2 h \]

where:

  • \( r \) is the radius of the base,
  • \( h \) is the height of the cone,
  • \( \pi \) is approximately \( 3.14159 \).

Given:

  • Radius \( r = 13 \) cm
  • Height \( h = 27 \) cm

Plugging in the values:

\[ V = \frac{1}{3} \pi (13)^2 (27) \]

Calculating \( (13)^2 \):

\[ (13)^2 = 169 \]

Now substitute back into the equation:

\[ V = \frac{1}{3} \pi (169)(27) \]

Calculating \( 169 \times 27 \):

\[ 169 \times 27 = 4563 \]

Now substitute this back into the volume equation:

\[ V = \frac{1}{3} \pi (4563) \]

Dividing by 3:

\[ \frac{4563}{3} = 1521 \]

Thus:

\[ V = 1521 \pi \]

To find a numerical approximation, use \( \pi \approx 3.14159 \):

\[ V \approx 1521 \times 3.14159 \approx 4779.32 \]

Rounding to the nearest tenth:

\[ \boxed{4779.3} \text{ cm}^3 \]

The volume of the cone is approximately \( 4779.3 \text{ cm}^3 \).