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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-11-CNV-01
Conversion of Solids — Assignment
Chapter: Mensuration
Topic: Conversion of Solids from One Shape to Another
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.
On melting and recasting, the conserved quantity is:
  • A.area
  • B.volume
  • C.height
  • D.radius
2.
When making small spheres from a big one, total volume:
  • A.increases
  • B.stays the same
  • C.decreases
  • D.doubles
3.
Number of recast items $=$
  • A.total area $\div$ item area
  • B.total volume $\div$ item volume
  • C.radius $\div$ height
  • D.$1$
4.
Recasting preserves:
  • A.shape
  • B.volume
  • C.surface area
  • D.nothing
5.
Volume of metal in a hollow pipe $=$
  • A.outer $+$ inner
  • B.outer $-$ inner volume
  • C.outer only
  • D.inner only
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
A sphere of radius $3$ is melted; what is conserved?
7.
A big cube of volume $64$ is cut into unit cubes; how many?
8.
A cylinder of volume $100$ is recast into cones of volume $5$; how many cones?
9.
State the principle used in conversion problems.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A metallic sphere of radius $6$ cm is melted into a cylinder of radius $4$ cm. Find the height.
11.
How many lead balls of radius $1$ cm can be made from a sphere of radius $8$ cm?
12.
A cone of radius $6$ and height $24$ is melted into a sphere. Find the sphere's radius.
13.
A cylinder of radius $6$ and height $15$ is recast into small cylinders of radius $1.5$ and height $2$. How many?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A solid metallic sphere of radius $10.5$ cm is melted and recast into cones of radius $3.5$ cm and height $3$ cm. Find the number of cones.
15.
A well of diameter $3$ m is dug $14$ m deep; the earth is spread to form a platform $22$ m by $14$ m. Find the height of the platform.

Answer Key

Section A — Multiple Choice Questions
  1. (B) volume
  2. (B) stays the same
  3. (B) total volume $\div$ item volume
  4. (B) volume
  5. (B) outer $-$ inner volume
Section B — Short Answer (2 marks)
  1. Volume.
  2. $64$.
  3. $20$.
  4. Conservation of volume.
Section C — Short Answer (3 marks)
  1. $18$ cm.
  2. $512$.
  3. $6$ cm.
  4. $120$.
Section D — Long Answer (5 marks)
  1. $126$.
  2. $\approx0.32$ m.
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