Question : If the base radius and the height of a right circular cone are increased by 10%, then the percentage increase in the volume is:

Option 1: 30.2%

Option 2: 22.1%

Option 3: 33.1%

Option 4: 20.2%

Question : Which of the following statements is not correct?

Option 1: For a given radius and height, a right circular cone has a lesser volume than a right circular cylinder.

Option 2: If the side of a cube is increased by 10%, the volume will increase by 33.1%.

Option 3: If the radius of a sphere is increased by 20%, the surface area will increase by 40%.

Option 4: Cutting a sphere into 2 parts does not change the total volume.

Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm³, then what is the slant height of the cone? (Use $\pi$ = 3.14)

Option 1: 12 cm

Option 2: 11 cm

Option 3: 13 cm

Option 4: 14 cm

Question : A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?

Option 1: 2 : 1

Option 2: 3 : 2

Option 3: 1 : 2

Option 4: 2 : 3

Question : The curved surface area of a right circular cone is $156 \pi$ and the radius of its base is 12 cm. What is the volume of the cone, in cm³?

Option 1: $192 \pi$

Option 2: $210 \pi$

Option 3: $240 \pi$

Option 4: $180\pi$