The radius of the base of a right circular cone is 6 cm and its slant height is 10 cm. Using π = 22/7, what is the volume of the cone in cubic centimetres?

Introduction / Context:

This question checks your understanding of the geometry of a right circular cone and the relation between radius, height, and slant height. It also tests whether you can correctly apply the volume formula for a cone and use the Pythagoras theorem to find the missing perpendicular height from the given slant height and radius.

Given Data / Assumptions:

• Radius of the base r = 6 cm.
• Slant height l = 10 cm.
• We are told to use π = 22/7.
• We must find the volume of the cone in cubic centimetres.

Concept / Approach:

The volume of a right circular cone is given by V = (1/3) * π * r^2 * h, where h is the perpendicular height. We are given the slant height, not h, so we must first use the Pythagoras theorem in the right triangle formed by radius, height, and slant height: l^2 = r^2 + h^2.

Step-by-Step Solution:

Verification / Alternative check:

You can approximate 2112 divided by 7. Since 7 * 300 = 2100 and 7 * 1.71 ≈ 11.97, the total is about 2111.97, which matches 2112 closely. This confirms that 301.71 cm3 is a good approximation.

Why Other Options Are Wrong:

The values 310.71 cm3 and 310.17 cm3 are too large and usually arise from errors in applying the (1/3) factor or misusing π. The value 301.17 cm3 is too small, coming from rounding mistakes. The value 280.00 cm3 results from missing the π factor or using incomplete multiplication.

Common Pitfalls:

Learners sometimes confuse slant height with perpendicular height and directly use 10 cm in the volume formula. Another common mistake is forgetting the factor of 1/3 that is specific to cone volume.

Final Answer:

The volume of the cone is approximately 301.71 cm3.