Surface Areas and Volumes

Topics in this chapter

• Surface Area Formulas
• Volume and Capacity
• Cubes, Cuboids and Cylinders
• Cones, Frustums and Slant Height
• Spheres and Hemispheres
• Composite and Combined Solids
• Recasting and Volume Conservation
• Applied Mensuration Problems

Cheat sheet

Practice questions

1. Question 1Q-7F97CF

   If the radius of the base of a right circular cylinder is halved, keeping the height the same, the ratio of the volume of the reduced cylinder to that of the original cylinder is:

   1. A.1 : 2
   2. B.1 : 4
   3. C.1 : 8
   4. D.2 : 1
   See the answer and solution
2. Question 2Q-953AC1

   A solid piece of iron in the form of a cuboid of dimensions $49 \text{ cm} \times 33 \text{ cm} \times 24 \text{ cm}$ is molded to form a solid sphere. What is the radius of the sphere? (Take $\pi = \frac{22}{7}$)

   1. A.21 cm
   2. B.28 cm
   3. C.14 cm
   4. D.35 cm
   See the answer and solution
3. Question 3Q-AF0CA9

   How many solid spherical bullets, each of diameter $4 \text{ cm}$, can be made out of a solid rectangular lead block of dimensions $22 \text{ cm} \times 12 \text{ cm} \times 5 \text{ cm}$? (Take $\pi = \frac{22}{7}$)

   1. A.315
   2. B.312.5
   3. C.310
   4. D.320
   See the answer and solution
4. Question 4Q-64A698

   If two solid hemispheres of same base radius $r$ are joined together along their bases, then the curved surface area of this new solid is:

   1. A.2\pi r^2
   2. B.3\pi r^2
   3. C.4\pi r^2
   4. D.6\pi r^2
   See the answer and solution
5. Question 5Q-B2C74A

   A cone and a cylinder have the same base radius and the same height. If the volume of the cylinder is $300 \text{ cm}^3$, then find the volume of the cone.

   1. A.100 cm³
   2. B.150 cm³
   3. C.900 cm³
   4. D.600 cm³
   See the answer and solution