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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-11-FRU-01
Frustum of a Cone — Assignment
Chapter: Mensuration
Topic: Frustum of a Cone
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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.
A frustum results from a cut:
  • A.through the apex
  • B.parallel to the base
  • C.perpendicular
  • D.oblique
2.
Volume of a frustum $=$
  • A.$\tfrac13\pi h(R^2+Rr+r^2)$
  • B.$\pi h(R+r)$
  • C.$\tfrac13\pi r^2h$
  • D.$\pi Rl$
3.
Slant height of a frustum $=$
  • A.$\sqrt{h^2+R^2}$
  • B.$\sqrt{h^2+(R-r)^2}$
  • C.$h+R$
  • D.$\sqrt{R^2-r^2}$
4.
CSA of a frustum $=$
  • A.$\pi(R+r)l$
  • B.$\pi(R-r)l$
  • C.$2\pi rl$
  • D.$\pi r^2$
5.
A frustum has two circular ends of radii:
  • A.$R$ only
  • B.$R$ and $r$
  • C.$r$ only
  • D.equal radii
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the slant height if $h=4,\ R=5,\ r=2$.
7.
State the volume formula of a frustum.
8.
Find the CSA of a frustum with $R=6,\ r=3,\ l=5$.
9.
Find $R+r$ for a frustum with radii $4$ and $2$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the volume of a frustum with $R=10,\ r=4,\ h=9$ ($\pi=3.14$).
11.
Find the slant height of a frustum with $R=8,\ r=5,\ h=4$.
12.
Find the CSA of a frustum with $R=6,\ r=3$ and slant height $5$.
13.
A bucket (frustum) has radii $15$ and $5$ and height $24$. Find its slant height.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A bucket is a frustum with radii $20$ cm and $12$ cm and height $15$ cm. Find its capacity ($\pi=3.14$).
15.
The radii of the ends of a frustum are $14$ cm and $6$ cm, and its height is $6$ cm. Find its curved surface area ($\pi=\tfrac{22}{7}$).

Answer Key

Section A — Multiple Choice Questions
  1. (B) parallel to the base
  2. (A) $\tfrac13\pi h(R^2+Rr+r^2)$
  3. (B) $\sqrt{h^2+(R-r)^2}$
  4. (A) $\pi(R+r)l$
  5. (B) $R$ and $r$
Section B — Short Answer (2 marks)
  1. $5$.
  2. $\tfrac13\pi h(R^2+Rr+r^2)$.
  3. $45\pi$.
  4. $6$.
Section C — Short Answer (3 marks)
  1. $\approx1469.52$ cm$^3$.
  2. $5$.
  3. $45\pi$.
  4. $26$ cm.
Section D — Long Answer (5 marks)
  1. $\approx12308.8$ cm$^3$ ($\approx12.3$ litres).
  2. $\approx628.57$ cm$^2$.
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