Mensuration 3D

Question 11

Given: A cylindrical container of radius 4 cm contains some fluid. A solid sphere of radius 3 cm is lowered into the fluid until it is completely immersed in it. Find by how the level of fluid in the vessel will rise.

• 5/8 cm

• 9/4 cm

• 3/7 cm

• 9/13 cm

Question 12

Given: A welder has a solid piece of iron of dimensions 49 * 33 * 24 cm³ which he will be molding into a sphere. What will be the radius of the sphere?

• 17/4 cm

• 20 cm

• 21 cm

• None of these

Question 13

Given: If three metallic spheres of iron, steel, and aluminium of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, find the diameter of the new sphere formed.

• 12.5 cm

• 18.7 cm

• 24 cm

• 30 cm

Question 14

The volumes of two sphere are in the ratio of 64:27. The ratio of their surface areas is:

• 1:2
• 2:3
• 9:16
• 16:9

Question 15

Given: The radii of two cones of copper and aluminium are in the ratio of 3:7, consider their volumes to be equal. Find the ratio of their heights.

• 9:49

• 3:7

• 49:9

• 7:3

Question 16

What is the matrix that represents rotation of an object by θ degree about the origin in 2D?

• cos θ    −sin θ
  sin θ     cos θ

• sin θ   −cos θ
  cos θ    sin θ

• cos θ   −sin θ
  cos θ    sin θ

• sin θ   −cos θ
  cos θ    sin θ