Answer :
Final answer:
The volume of the cone with a radius of 6 inches and a height of 10 inches is 120π in³, calculated using the formula for the volume of a cone.
Explanation:
The volume of a cone can be calculated using the formula V = ⅓πr²h, where V is the volume, r is the radius, and h is the height of the cone. In the given problem, the radius (r) is 6 inches and the height (h) is 10 inches.
- First, calculate the area of the base using the formula for the area of a circle, A = πr². So, A = π × 6² = 36π in².
- Next, use the volume formula for a cone. V = ⅓π × 36 in² × 10 in = ⅓ × 360π in³ = 120π in³.
So, the volume of the cone is 120π in³.
Final answer:
The volume of the cone with a radius of 6 inches and height of 10 inches is 120π in.³.
Explanation:
The volume of a cone is given by the formula V = (1/3) πr²h, where r is the radius of the base of the cone, h is the height of the cone, and π (pi) is a mathematical constant approximately equal to 3.14159.
In this case, the radius (r) of the cone is 6 inches and the height (h) is 10 inches. Using the formula:
- V = (1/3) π × (6 in.)² × 10 in.
- V = (1/3) π × 36 in.² × 10 in.
- V = (1/3) × 360 π in.³
- V = 120π in.³
Therefore, the volume of the cone is 120π in.³.
