Exams › SSC CGL (Prelims) › General

A cone has its base area equal to its lateral surface area. If the radius is \(r\), find the slant height \(l\).

1. r
2. 2r
3. 3r
4. 4r

Correct answer: 2r

Solution

Base area of a cone is \(\pi r^2\) and lateral surface area is \(\pi r l\). Since they are equal, \(\pi r^2 = \pi r l\), which gives \(l = r\). However, the provided options do not include this correct result, so the intended option appears inconsistent.

Related SSC CGL (Prelims) General questions

• A right circular cone has a radius of 9 cm and a height of 40 cm. What is its slant height?
• A rectangular prism has a base area of 36 cm². If its height is increased by 25% from the original height of 12 cm, what is the new volume?
• A solid metal sphere of radius 6 cm is completely immersed in a vertical cylindrical vessel containing water, causing the water level to rise by 4 cm. What is the radius of the cylinder?
• A gardener has 80 m of fencing wire. He can use this wire to enclose either a circular lawn or a square lawn. If he uses the entire wire in each case, what is the approximate ratio of the area of the circular lawn to the area of the square lawn?
• A sector of a circle has a central angle of 150° and radius 10 cm. Another sector of the same circle has a central angle of \(\frac{5\pi}{6}\) radians. What is the ratio of the area of the first sector to that of the second?
• What is the area of a sector of a circle with radius 9 cm and central angle 80°?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →