5 Problems - SHOW ALL WORK!
1. What is the formula to find the volume of a cone?
2. Find the volume of the cone: 10 IN height 4 IN radius
3. Find the volume of the cone. Round to the nearest tenth.
Diameter: 10cm
Height: 14cm
4.A cone that is 12 across and 6 high. What is the volume?
5. How would changing the dimensions affect the volume of the cone? Give specific examples.
1. The formula to find the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
2. V = (1/3)π(4^2)(10) = (1/3)π(16)(10) = (1/3)(160)π = 53.33π cubic inches
3. First, we need to find the radius. Radius = diameter/2 = 10cm/2 = 5cm
V = (1/3)π(5^2)(14) = (1/3)π(25)(14) = (1/3)(350)π = 116.67π ≈ 366.5 cubic cm
4. Radius = 12/2 = 6
V = (1/3)π(6^2)(6) = (1/3)π(36)(6) = (1/3)(216)π = 72π cubic units
5. Changing the radius or the height of the cone would affect the volume. For example:
- If the radius is doubled, the volume increases by a factor of 4
- If the height is halved, the volume would also be halved
- If both the radius and height are doubled, the volume would increase by a factor of 8.