Q.A solid cylindrical iron rod has a cross-sectional diameter of 16 cm and a length of 1 meter. If this rod is melted and used to form right circular cones, each with a height of 4 cm and a base radius of 5 cm, how many such cones can be made?

The radius of the solid cylindrical iron rod's cross-section is \[ \frac{16}{2} \text{ cm} = 8 \text{ cm} \] and its length is \[ 1 \text{ meter} = 100 \text{ cm} \] Therefore, the volume of the iron rod is: \[ π × 8^2 × 100 = π × 64 × 100 \text{ cubic cm} \] Volume of each cone: \[ \frac{1}{3} × π × 5^2 × 8 = \frac{1}{3} × π × 25 × 8 \text{ cubic cm} \] Let \(x\) be the number of cones formed. According to the question: \[ \frac{1}{3} × π × 25 × 8 × x = π × 64 × 100 \] Canceling π from both sides and simplifying: \[ \frac{25 × 8}{3}x = 64 × 100 \Rightarrow x = \frac{64 × 100 × 3}{25 × 8} \Rightarrow x = 96 \] Therefore, 96 solid cones can be formed.
Similar Questions