1. To find the diameter of the cone, we can use the formula for the slant height of a cone, which is calculated as √(r^2 + h^2), where r is the radius and h is the height of the cone. Given that the height is 10 inches and the radius is 4 inches, we can plug these values into the formula to find the slant height.
slant height = √(4^2 + 10^2) = √(16 + 100) = √116 ≈ 10.77 inches
Now that we have the slant height, we can calculate the diameter by doubling the radius:
diameter = 2 * radius = 2 * 4 = 8 inches
Therefore, the diameter of the cone is 8 inches.
2. To find the radius of the cylinder, we simply divide the diameter by 2 since the radius is half the diameter. Given that the height of the cylinder is 11.2 feet and the diameter is 5.2 feet, we can calculate the radius:
radius = diameter / 2 = 5.2 / 2 = 2.6 feet
Therefore, the radius of the cylinder is 2.6 feet.
3. Difference and Similarity between a cone and a cylinder:
- Differences:
- Shape: A cone has a circular base that tapers to a point while a cylinder has two parallel circular bases.
- Volume: The volume formula for a cone is (1/3)πr^2h while the volume formula for a cylinder is πr^2h. This means that a cone has one-third the volume of a cylinder with the same base and height.
- Similarity:
- Both have curved surfaces and are three-dimensional shapes.
- Both have a circular base.
1. What is the diameter of the cone below: 10 in (h), 4 in
2. What is the radius of the cylinder below: 5.2 ft , 11.2 ft (h)
3. Explain the difference and similarity of a cone and a cylinder.
1 answer