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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-13-CT
Surface Areas and Volumes — Full Chapter Test
Chapter: Surface Areas and Volumes
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Volume of a cube of edge $a$:
  • A.$6a^2$
  • B.$a^3$
  • C.$3a^2$
  • D.$a^2$
2.
Volume of a combined solid $=$
  • A.largest part
  • B.sum of parts' volumes
  • C.difference
  • D.average
3.
$1$ m $=$
  • A.$10$ cm
  • B.$100$ cm
  • C.$1000$ cm
  • D.$10000$ cm
4.
Surface area of a sphere:
  • A.$4\pi r^2$
  • B.$2\pi r^2$
  • C.$\pi r^2$
  • D.$\tfrac43\pi r^3$
5.
Surface area of a combined solid uses the ___ surfaces.
  • A.hidden
  • B.exposed
  • C.flat
  • D.inner
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the volume of a cube of edge $5$ cm.
7.
Find the CSA of a hemisphere of radius $7$ ($\pi=\tfrac{22}{7}$).
8.
Convert $2$ m to cm.
9.
Find the volume of a cylinder, $r=7$, $h=10$ (use $\pi=\tfrac{22}{7}$).
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the total surface area of a cuboid $8\times6\times5$.
11.
A toy is a cone on a hemisphere, both of radius $7$ cm; the cone's height is $24$ cm. Find the cone's slant height.
12.
A tank holds $5$ m$^3$ of water. Express this in litres.
13.
Find the volume of a sphere of radius $21$ cm ($\pi=\tfrac{22}{7}$).
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A cylindrical tank has radius $7$ m and height $10$ m. Find its volume and curved surface area ($\pi=\tfrac{22}{7}$).
15.
A circus tent is cylindrical to height $3$ m and conical above. Base radius $14$ m, cone slant height $15$ m. Find the canvas (curved) area ($\pi=\tfrac{22}{7}$).

Answer Key

Section A — Multiple Choice Questions
  1. (B) $a^3$
  2. (B) sum of parts' volumes
  3. (B) $100$ cm
  4. (A) $4\pi r^2$
  5. (B) exposed
Section B — Short Answer (2 marks)
  1. $125$ cm$^3$.
  2. $308$ cm$^2$.
  3. $200$ cm.
  4. $1540$ cm$^3$.
Section C — Short Answer (3 marks)
  1. $236$ cm$^2$.
  2. $25$ cm.
  3. $5000$ L.
  4. $38808$ cm$^3$.
Section D — Long Answer (5 marks)
  1. Volume $1540$ m$^3$; CSA $440$ m$^2$.
  2. $924$ m$^2$.
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