Question

In the following question, two statements, (i) and (ii), are given. Choose the valid statement.

1. The radius and height of a core are in the ratio 3 : 4 and its volume is 301.44 cm³. If π = 3.14, then its radius will be 6 cm.
2. Volume of cylinder = `1/3πr^2h`

Options

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (i)

Explanation:

Statement (i) is valid because substituting r = 3x and h = 4x into the cone volume formula gives `1/3 × 3.14 × 9x^2 × 4x` = 301.44, which simplifies to x³ = 8 or x = 2, confirming a radius of 3(2) = 6 cm. Statement (ii) is invalid because `1/3πr^2 h` is the formula for the volume of a cone, not a cylinder.