Answer: Option A
Given information:The area of the base of a right circular cone is 78.5 cm^2.Height of the cone = 12 cm.
To find:The volume of the cone.
Solution:We know that the formula for the volume of a cone is given by:
V = (1/3)πr^2h,
where r is the radius of the base and h is the height of the cone.
Since the base of the cone is a circle, the area of the base is given by:
A = πr^2,
where A is the given area of the base.
Let's substitute the given values in the equation for the area of the base of the cone:
78.5 = πr^2
r^2 = 78.5/π
r^2 ≈ 25
r ≈ 5
Now that we have the value of the radius, we can substitute it in the equation for the volume of the cone:
V = (1/3)πr^2h
V = (1/3)π(5^2)(12)
V ≈ 314 cm^3
Therefore, the correct answer is option A, 314 cm^3.
Explanation:

• A cone is a three-dimensional shape that tapers smoothly from a flat, usually circular base to a point called the apex or vertex.
• A right circular cone is a cone where the axis of the cone is perpendicular to the base and the base is a circle.
• The volume of a right circular cone is given by the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
• The area of the base of a right circular cone is given by the formula A = πr^2, where A is the area of the base and r is the radius of the base.
• To find the volume of a cone, we need to know the area of the base and the height of the cone.
• In this question, we are given the area of the base and the height of the cone, and we use these values to find the radius of the base and the volume of the cone.
• The correct answer is option A, 314 cm^3.

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