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3 problems match “volumes of revolution”. Clear

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1. Base area of a cone-cylinder solid ●●○○○ 20 ptsA solid consists of a cone on top of a cylinder, where the cylinder and the cone have the same radius. The height of the cone is 18 and the height of the cylinder is 1. If the volume of the solid is $49\pi$, find the area of the base of the cylinder. Round to two decimal places.
2. Difference of cone volumes from a triangle ●●○○○ 20 ptsA right-angled triangle with sides 6 cm, 8 cm and 10 cm is revolved about each of the two sides that contain the right angle, giving two solids. Find the difference between their volumes in cm$^3$. Round to two decimal places.
3. Hypotenuse from two cone volumes ●●●○○ 50 ptsWhen a right triangle is rotated about one leg, the volume of the cone produced is $800\pi \text{ cm}^3$. When the triangle is rotated about the other leg, the volume of the cone produced is $1920\pi \text{ cm}^3$. What is the length (in cm) of the hypotenuse of the triangle?