Exams › SSC CGL (Prelims) › General

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?

1. 4 √ 2 cm
2. 5 √ 2 cm
3. 6 √ 2 cm
4. 8 √ 2 cm

Correct answer: 6 √ 2 cm

Solution

When the sphere is immersed, it displaces water equal to its own volume. So, volume of sphere = volume of cylindrical water rise: $\frac{4}{3}\pi(6)^3 = \pi r^2 \times 4$. Solving gives $r^2=72$, hence $r=6\sqrt{2}$ cm.

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 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°?
• The area of a sector of a circle of radius 6 cm with central angle \(120^\circ\) is:

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