Surface Areas and Volumes - Short Revision || CBSE Class 10 Mathematics || Infinity Learn Class 9&10

TL;DR

This content provides multiple-choice questions related to surface areas and volumes, covering topics such as cylinders, spheres, cones, and hemispheres.

Transcript

now let's do some mcqs in the chapter surface areas and volumes so let's start with it so if the radius of base of a right circular cylinder is halved keeping the height the same then the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder is what so let's do it guys so what is the volume in the first case see s... Read More

Key Insights

• 🔇 Volume is directly proportional to the square of the radius in a cylinder.
• 😮 The rise in water level is equal to the volume of the submerged sphere.
• 🥳 The largest right circular cone inside a cube has a ratio of 1:2 for its radius and height.

Questions & Answers

Q: What is the volume ratio of a cylinder when the radius is halved but the height remains the same?

The volume of the cylinder is directly proportional to the square of the radius. Therefore, if the radius is halved, the volume becomes one-fourth of the original cylinder.

Q: What is the rise in water level when a sphere with a diameter of 13 cm is dropped into a cylindrical vessel with a diameter of 36 cm?

The rise in water level is equal to the volume of the sphere. By substituting the given values into the formula, the rise in water level is determined to be 3 cm.

Q: What is the ratio of the radius and height of the largest right circular cone that can be cut out from a cube?

The largest cone that can fit inside the cube will have a height equal to its radius. Therefore, the ratio of the radius and height is 1:2.

Q: Given the surface area of a sphere as 616 cm², what is its radius?

By using the formula for the surface area of a sphere, the value of the radius can be calculated as 7 cm.

Summary & Key Takeaways

• The first question involves finding the volume ratio of a cylinder when the radius is halved and the height remains the same.

• The second question asks for the rise in water level when a sphere is dropped into a cylindrical vessel partially filled with water.

• The third question deals with finding the ratio of the radius and height of the largest right circular cone that can be cut out from a cube.

• The fourth question requires finding the radius of a sphere given its surface area.