Vidaara.orgClass 9 · Mathematics
CodeVID-M09-13-CMB-01
Combined Solids - Assignment
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.
Volume of a combined solid $=$
- A.largest part
- B.sum of parts' volumes
- C.difference
- D.average
2.
Surface area of a combined solid uses the ___ surfaces.
- A.hidden
- B.exposed
- C.flat
- D.inner
3.
CSA of a hemisphere $=$
- A.$\pi r^2$
- B.$2\pi r^2$
- C.$3\pi r^2$
- D.$4\pi r^2$
4.
TSA of a solid hemisphere $=$
- A.$2\pi r^2$
- B.$3\pi r^2$
- C.$\pi r^2$
- D.$4\pi r^2$
5.
A cone mounted on a cylinder is an example of a:
- A.single solid
- B.combined solid
- C.plane figure
- D.net
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the CSA of a hemisphere of radius $7$ ($\pi=\tfrac{22}{7}$).
7.
Find the volume of a hemisphere of radius $3$ (in terms of $\pi$).
8.
How is the volume of a combined solid found?
9.
Find the TSA of a solid hemisphere of radius $7$ ($\pi=\tfrac{22}{7}$).
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
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.
11.
Find the volume of a hemisphere of radius $3$ cm (in terms of $\pi$).
12.
A cylinder ($r=7$, $h=10$) is surmounted by a cone ($r=7$, $h=24$). Find the total volume ($\pi=\tfrac{22}{7}$).
13.
Find the CSA of a cone with $r=7$, $l=25$ ($\pi=\tfrac{22}{7}$).
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
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 ($\pi=\tfrac{22}{7}$).
15.
A vessel is a cylinder ($r=7$ cm, $h=20$ cm) surmounted by a cone (same radius, height $9$ cm). Find the total volume ($\pi=\tfrac{22}{7}$).
Answer Key
Section A — Multiple Choice Questions
- (B) sum of parts' volumes
- (B) exposed
- (B) $2\pi r^2$
- (B) $3\pi r^2$
- (B) combined solid
Section B — Short Answer (2 marks)
- $308$ cm$^2$.
- $18\pi$ cm$^3$.
- By adding the volumes of its parts.
- $462$ cm$^2$.
Section C — Short Answer (3 marks)
- $25$ cm.
- $18\pi$ cm$^3$.
- $2772$ cm$^3$.
- $550$ cm$^2$.
Section D — Long Answer (5 marks)
- $924$ m$^2$.
- $3542$ cm$^3$.
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