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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-11-CT
Mensuration — Full Chapter Test
Chapter: Mensuration
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 cylinder $=$
  • A.$\pi r^2h$
  • B.$\tfrac13\pi r^2h$
  • C.$2\pi rh$
  • D.$\tfrac43\pi r^3$
2.
A frustum results from a cut:
  • A.through the apex
  • B.parallel to the base
  • C.perpendicular
  • D.oblique
3.
On melting and recasting, the conserved quantity is:
  • A.area
  • B.volume
  • C.height
  • D.radius
4.
Volume of a cone $=$
  • A.$\pi r^2h$
  • B.$\tfrac13\pi r^2h$
  • C.$\tfrac43\pi r^3$
  • D.$2\pi r^2$
5.
Volume of a frustum $=$
  • A.$\tfrac13\pi h(R^2+Rr+r^2)$
  • B.$\pi h(R+r)$
  • C.$\tfrac13\pi r^2h$
  • D.$\pi Rl$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the volume of a cylinder with $r=7,\ h=10$ ($\pi=\tfrac{22}{7}$).
7.
Find the slant height if $h=4,\ R=5,\ r=2$.
8.
A sphere of radius $3$ is melted; what is conserved?
9.
Find the volume of a sphere of radius $3$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the total surface area of a cylinder with $r=7,\ h=10$.
11.
Find the volume of a frustum with $R=10,\ r=4,\ h=9$ ($\pi=3.14$).
12.
A metallic sphere of radius $6$ cm is melted into a cylinder of radius $4$ cm. Find the height.
13.
Find the total surface area of a cone with $r=6,\ l=10$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A solid is a cylinder ($r=7$, height $10$ cm) with a cone ($r=7$, height $6$ cm) on top. Find the total volume ($\pi=\tfrac{22}{7}$).
15.
A bucket is a frustum with radii $20$ cm and $12$ cm and height $15$ cm. Find its capacity ($\pi=3.14$).

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\pi r^2h$
  2. (B) parallel to the base
  3. (B) volume
  4. (B) $\tfrac13\pi r^2h$
  5. (A) $\tfrac13\pi h(R^2+Rr+r^2)$
Section B — Short Answer (2 marks)
  1. $1540$ cm$^3$.
  2. $5$.
  3. Volume.
  4. $36\pi$.
Section C — Short Answer (3 marks)
  1. $748$ cm$^2$.
  2. $\approx1469.52$ cm$^3$.
  3. $18$ cm.
  4. $96\pi$.
Section D — Long Answer (5 marks)
  1. $1848$ cm$^3$.
  2. $\approx12308.8$ cm$^3$ ($\approx12.3$ litres).
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