Question$\text{The diagram shows a solid cone with radius } 7.6 \text{ cm and height } 16 \text{ cm.}$ $\text{A cut is made parallel to the base of the cone and the top section is removed.}$ $\text{The remaining solid has height } 12 \text{ cm as shown in the diagram.}$ $\text{Find the volume of the remaining shape.}$

Studdy Solution
Subtract the volume of the smaller cone from the volume of the original cone to find the volume of the frustum:
$$V_{\text{frustum}} = V_{\text{original}} - V_{\text{small}}$$
The volume of the remaining shape (frustum) is:
$$V_{\text{frustum}} = \frac{1}{3} \pi (7.6)^2 (16) - \frac{1}{3} \pi (1.9)^2 (4)$$
$$V_{\text{frustum}} = \frac{1}{3} \pi [ (7.6)^2 (16) - (1.9)^2 (4) ]$$
$$V_{\text{frustum}} = \frac{1}{3} \pi [ 921.6 - 14.44 ]$$
$$V_{\text{frustum}} = \frac{1}{3} \pi \times 907.16$$
$$V_{\text{frustum}} \approx 951.28 \text{ cm}^3$$
$$\boxed{951.28 \text{ cm}^3}$$