Question

Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm 
(ii) radius 3.5 cm, height 12 cm

Answer 1

We are given two cases of right circular cones. We need to calculate their volumes.

Step-by-Step Solution:

1. Formula for the Volume of a Cone:

The volume \( V \) of a cone is given by the formula: \[ V = \frac{1}{3} \pi r^2 h \] where: - \( r \) is the radius of the base, - \( h \) is the height of the cone.

(i) Case 1: Radius = 6 cm, Height = 7 cm

Substituting the values \( r = 6 \, \text{cm} \) and \( h = 7 \, \text{cm} \) into the formula: \[ V = \frac{1}{3} \pi (6^2) (7) \] \[ V = \frac{1}{3} \times 3.14 \times 36 \times 7 \] \[ V = \frac{1}{3} \times 3.14 \times 252 \] \[ V = \frac{1}{3} \times 791.88 = 263.96 \, \text{cm}^3 \] So, the volume of the cone is approximately \( 263.96 \, \text{cm}^3 \).

(ii) Case 2: Radius = 3.5 cm, Height = 12 cm

Substituting the values \( r = 3.5 \, \text{cm} \) and \( h = 12 \, \text{cm} \) into the formula: \[ V = \frac{1}{3} \pi (3.5^2) (12) \] \[ V = \frac{1}{3} \times 3.14 \times 12.25 \times 12 \] \[ V = \frac{1}{3} \times 3.14 \times 147 \] \[ V = \frac{1}{3} \times 461.58 = 153.86 \, \text{cm}^3 \] So, the volume of the cone is approximately \( 153.86 \, \text{cm}^3 \).

Final Answers:

• Volume of the first cone = \( \boxed{263.96 \, \text{cm}^3} \)
• Volume of the second cone = \( \boxed{153.86 \, \text{cm}^3} \)