ind the volume of a frustum of a cone  with bases radii 52 cm and 42 cm. Slant height is 95 cm. Answer tolerancy limits have been set ± 10 cm3.

To find the volume of a frustum of a cone, we use the following formula:

\[
V = \frac{1}{3} \pi h \left(R^2 + r^2 + R \cdot r\right)
\]

Where:
- \( V \) = volume of the frustum
- \( R \) = radius of the larger base (52 cm)
- \( r \) = radius of the smaller base (42 cm)
- \( h \) = height of the frustum (to be calculated from the slant height)

### Step 1: Calculate the height of the frustum
We have the slant height \( l = 95 \) cm. Using the Pythagorean theorem, we can calculate the height \( h \) of the frustum:
\[
l^2 = h^2 + (R - r)^2
\]
Substitute the values:
\[
95^2 = h^2 + (52 - 42)^2
\]
\[
9025 = h^2 + 10^2
\]
\[
9025 = h^2 + 100
\]
\[
h^2 = 8925
\]
\[
h = \sqrt{8925} \approx 94.52 \, \text{cm}
\]

### Step 2: Calculate the volume of the frustum
Now, we can substitute the values into the formula:
\[
V = \frac{1}{3} \pi (94.52) \left(52^2 + 42^2

Find the volume of a frustum of a cone with bases radii 52 cm and 42 cm. Slant height is 95 cm. Answer tolerancy limits have been set ± 10 cm³.

Learn how to calculate the volume of a frustum of a cone with larger base radius 52 cm, smaller base radius 42 cm, and a slant height of 95 cm. This solution covers the geometry of 3D shapes, using the volume formula for a frustum and the Pythagorean theorem for height calculation. Suitable for high school geometry students.

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