STATEMENT – 1: The slant height of frustum of cone is 4cm. and perimeter of its circular ends are 18 cm, and 6 cm, then the curved surface area is 48 sq. cm.

STATEMENT – 2: Curved surface area of frustum is π (r₁ + r₂) where r₁ and r₂ are the radii of the frustum and l is the slant height.

• (a) Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for statement - 1.
• (b) Statement - 1 is True, Statement - 2 is True, Statement - 2 is not a correct explanation for statement - 1.
• (c) Statement - 1 is True, Statement - 2 is False.
• (d) Statement - 1 is False, Statement - 2 is True.

To analyze the statements regarding the frustum of a cone, let's break down the information provided.

Understanding the Statements

Statement 1

The slant height of the frustum is given as 4 cm, and the perimeters of the circular ends are 18 cm and 6 cm. To find the radii, we can use the formula for the perimeter of a circle, which is C = 2πr. This gives us:

• For the larger base: r₁ = 18 / (2π)
• For the smaller base: r₂ = 6 / (2π)

Using these radii, we can calculate the curved surface area.

Statement 2

The formula for the curved surface area of a frustum is indeed π(r₁ + r₂)l, where l is the slant height. Plugging in the values:

• Curved Surface Area = π(r₁ + r₂) * 4

Calculating this gives us a curved surface area of 48 sq. cm, confirming that Statement 1 is true.

Evaluating the Options

Now, let's evaluate the options:

• (a) Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for statement - 1.
• (b) Statement - 1 is True, Statement - 2 is True, Statement - 2 is not a correct explanation for statement - 1.
• (c) Statement - 1 is True, Statement - 2 is False.
• (d) Statement - 1 is False, Statement - 2 is True.

Since both statements are true and Statement 2 correctly explains Statement 1, the correct choice is:

Final Answer

(a) Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for statement - 1.