Volume and Surface Area Formulas

The video tutorial covers multiple-choice questions (MCQs) on the topic of surface areas and volumes. It begins with a problem on the volume ratio of a cylinder when its radius is halved. Next, it addresses the rise in water level when a sphere is submerged in a cylindrical vessel. The tutorial then explores the largest cone that can fit inside a cube, followed by calculating the radius of a sphere given its surface area. Finally, it discusses the relationship between the volume and surface area of a solid hemisphere.

If the radius of the base of a right circular cylinder is halved while keeping the height constant, what is the ratio of the new volume to the original volume?

• 1:5

• 1:4

• 1:3

• 1:2

What is the formula for the volume of a right circular cylinder?

• 2πrh

• πr²h

• 2πr²h

• πr²

In the context of a right circular cylinder, if the radius is halved, what happens to the volume?

• It is halved

• It doubles

• It is reduced to a quarter

• It remains the same

What is the formula for the volume of a cylinder?

• 2πr²h

• πr²

• 2πrh

• πr²h

What happens to the volume of a cylinder if its radius is halved?

• It doubles

• It remains the same

• It is halved

• It is reduced to a quarter

When a sphere is submerged in a cylindrical vessel, what determines the rise in water level?

• The diameter of the sphere

• The volume of the sphere

• The surface area of the sphere

• The weight of the sphere

What is the relationship between the volume of a submerged sphere and the rise in water level in a cylinder?

• No relationship

• Rise is half the volume

• Volume is double the rise

• They are equal

If a sphere of radius 9 cm is submerged in a cylinder of radius 18 cm, what is the rise in water level?

• 1 cm

• 2 cm

• 3 cm

• 4 cm

What is the formula for the volume of a sphere?

• 3/4πr³

• πr²h

• 2/3πr³

• 4/3πr³

What is the effect on water level when a sphere is submerged in a cylinder?

• It decreases

• It remains the same

• It increases

• It fluctuates