The ratio of the base area of a hollow cone to that of its curved surface is 1:4. If its base radius is 7cm, calculate the slant height of the cone

Analyze the question

We are given a cone with base radius r = 7 cm. The ratio of base area to curved surface area is 1:4. We need the slant height l.

Concept

• Base area = πr²
• Curved surface area = πrl

Solution

Ratio: πr² : πrl = 1 : 4

Simplify the ratio by dividing both parts by πr:

r : l = 1 : 4

So l = 4r = 4 × 7 = 28 cm

Check:

• Base area = π(7)² = 49π
• Curved surface area = π(7)(28) = 196π
• 49π : 196π = 1 : 4 ✓

The "hollow" cone just tells us the base is an open or separate circle, and we still use the base area as πr² and the curved surface as πrl, so the working is unaffected.

Answer: C (28 cm).

Tip: For cone ratio questions, πr cancels out of "base area : curved area," leaving r : l. So the slant height is simply the ratio number multiplied by the radius, as in 4 × 7 here.