The following diagram shows the frustum of a cone. The top and bottom diameters are 6 cm and 18 cm…

Question

The following diagram shows the frustum of a cone. The top and bottom diameters are 6 cm and 18 cm respectively. Given that its perpendicular height is 15 cm, calculate the volume of the frustum.

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For question 11, we need to calculate the volume of the frustum.

Identify the given dimensions and calculate the radii.
The height of the frustum is $h = 10$ cm.
The top diameter is 6 cm, so the top radius is $r_1 = \frac{6}{2} = 3$ cm.
The bottom diameter is 18 cm, so the bottom radius is $r_2 = \frac{18}{2} = 9$ cm.
We are given $\pi = 3.142$ .
Write down the formula for the volume of a frustum.
The volume $V$ of a frustum is given by the formula:
$V = \frac{1}{3} \pi h (r_1^2 + r_1 r_2 + r_2^2)$
Substitute the values into the formula.
$V = \frac{1}{3} \times 3.142 \times 10 \times (3^2 + (3)(9) + 9^2)$
Calculate the terms inside the parenthesis.
$V = \frac{1}{3} \times 3.142 \times 10 \times (9 + 27 + 81)$ $V = \frac{1}{3} \times 3.142 \times 10 \times (117)$
Perform the multiplication to find the volume.
$V = 3.142 \times 10 \times \frac{117}{3}$ $V = 3.142 \times 10 \times 39$ $V = 31.42 \times 39$ $V = 1225.38 \text{ cm}^3$
The volume of the frustum is $\text{1225.38 cm}^3$ .

The following diagram shows the frustum of a cone. The top and bottom diameters are 6 cm and 18 cm respectively. Given that its perpendicular height is 15 cm, calculate the volume of the frustum.

Answer

Step-by-step solution

Identify the given dimensions and calculate the radii.

Write down the formula for the volume of a frustum.

Substitute the values into the formula.

Calculate the terms inside the parenthesis.

Perform the multiplication to find the volume.

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