# NCERT Mathematics Class 9 Exemplar Ch 13 Surface Areas and Volumes Part 3

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**Exercise 13.2**

Q.1. The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Answer: .True,

Q.2. If the radius of a right circular cone is halved and height is doubled, the volume will remain unchanged.

Answer: False, since new volume = (Original volume)

Q.3. In a right circular cone, height, radius and slant height do not always be sides of a right triangle.

Answer: True, since

Q.4. If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Answer: True,

Q.5. The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.

Answer: True, since volume of cone = volume of hemisphere

Q.6. A cylinder and a right circular cone are having the same base and same height. The volume of the cylinder is three times the volume of the cone.

Answer: True, since

Q.7. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is 1: 2: 3.

Answer: True,

Q.8. If the length of the diagonal of a cube is 6 3 cm, then the length of the edge of the cube is 3 cm.

Answer: False,

Q.9. If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6: π.

Answer: True, Radius of sphere (Volume of sphere)

Q.10. If the radius of a cylinder is doubled and height is halved, the volume will be doubled.

Answer: True, new volume Therefore, volume is doubled.