Chapter 9 Practice Paper: Volume and Surface Area of Pyramids, Cones and Spheres — question paper

Section A: Multiple-choice questions[10 marks]

Answer all questions. For each question, write the letter (A, B, C or D) of the correct answer in the brackets provided.

1. 1

   A pyramid’s volume is

   1. Aequal to the prism on the same base
   2. Bhalf of the prism on the same base
   3. Cone third of the prism on the same base
   4. Dthree times the prism on the same base
   ( )
2. 2

   With pi as 22/7, the volume of a cone of radius 3 and height 7 works out to

   1. A66 cm³
   2. B198 cm³
   3. C22 cm³
   4. D56 cm³
   ( )
3. 3

   The radius of a cone is 6 and its height is 8. Calculate the distance from apex to rim.

   1. A14
   2. B48
   3. C100
   4. D10
   ( )
4. 4

   With pi as 3.14, the surface area of a ball of radius 3 measures

   1. A38.46 cm²
   2. B113.04 cm²
   3. C339.12 cm²
   4. D12.56 cm²
   ( )
5. 5

   A sphere has radius 2. Taking pi as 3.14, its volume is closest to

   1. A25.12 cm³
   2. B16.75 cm³
   3. C33.5 cm³
   4. D50.24 cm³
   ( )
6. 6

   A pyramid stands on a square base of side 12 and rises 8. Its volume is

   1. A384 cm³
   2. B1 152 cm³
   3. C768 cm³
   4. D96 cm³
   ( )
7. 7

   For pi use 3.14. The wrap-around area of a cone with r = 5 and slant height 13 is

   1. A408.2 cm²
   2. B102.05 cm²
   3. C65 cm²
   4. D204.1 cm²
   ( )
8. 8

   Tripling a ball’s radius multiplies the space it fills by

   1. A3 times as big
   2. B27 times as big
   3. C9 times as big
   4. D6 times as big
   ( )
9. 9

   A closed cone has a base circle of radius 7 and a slant of 10. Using pi as 22/7, the entire surface adds up to

   1. A220 cm²
   2. B154 cm²
   3. C374 cm²
   4. D528 cm²
   ( )
10. 10

    A cylinder and a cone share the same radius and height. The cylinder’s volume is

    1. A3 times the cone’s
    2. Bthe same as the cone’s
    3. Cone third of the cone’s
    4. D2 times the cone’s
    ( )

Section B: Structured questions[20 marks]

Answer all questions in the spaces provided. Show your working clearly. Take pi as 22/7 or 3.14 as instructed in each question.

1. 1

   A glass ornament is a square pyramid with a base edge of 6 and a vertical height of 8.

   1. (a)

      Find the volume of the ornament.

      [2]
   2. (b)

      Each triangular face rises 8 from the middle of a base edge. Find the face height using Pythagoras, correct to 2 decimal places.

      [2]
   3. (c)

      Find the total area of the four triangular faces, correct to 1 decimal place.

      lateral area =[1]
2. 2

   A teepee tent is a cone with radius 7 and vertical height 24. Take pi as 22/7.

   1. (a)

      Find the slant height of the tent.

      [2]
   2. (b)

      Find the area of canvas needed to cover the curved surface (ignore the floor).

      [2]
   3. (c)

      Find the area of circular ground the tent covers.

      floor area =[1]
3. 3

   A spherical water tank has a radius of 30. Take pi as 3.14.

   1. (a)

      Find the volume of the tank, in cm³.

      [2]
   2. (b)

      Turn your answer from part (a) into litres.

      capacity =[1]
   3. (c)

      Find the surface area to be painted, in cm².

      [2]
4. 4

   An ice-cream cornet is a cone of radius 3 and height 14, topped by a hemispherical scoop of radius 3. Take pi as 22/7.

   1. (a)

      Compute the cone’s volume.

      [2]
   2. (b)

      Find the volume of the hemispherical scoop, correct to 2 decimal places.

      [2]
   3. (c)

      Add the two volumes for the whole cornet (2 d.p.).

      total =[1]