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CBSE · Class 9 · Mathematics

Math of Space: Surface Area and Volume

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
A cone has radius 14 cm and height 48 cm. Its slant height is:
  1. 51 cm
  2. 62 cm
  3. 34 cm
  4. 50 cm
2.
The curved surface area of a cone with radius 14 cm and slant height 50 cm (π = 22/7) is:
  1. 2,816 cm2
  2. 4,400 cm2
  3. 2,200 cm2
  4. 616 cm2
3.
The surface area of a sphere of radius 70 cm (π = 22/7) is:
  1. 1,437,333 1/3 cm2
  2. 30,800 cm2
  3. 46,200 cm2
  4. 61,600 cm2
4.
The total surface area of a solid hemisphere of radius 14 cm (π = 22/7) is:
  1. 2,464 cm2
  2. 1,232 cm2
  3. 1,848 cm2
  4. 1,862 cm2
5.
The curved surface area of a cone is:
  1. πrh
  2. πr2
  3. πrl
  4. 2πrh
6.
The volume of a sphere of radius 35 cm (π = 22/7) is:
  1. 179,666 2/3 cm3
  2. 539,000 cm3
  3. 15,400 cm3
  4. 89,833 1/3 cm3
7.
The volume of a cone with radius 21 cm and height 28 cm (π = 22/7) is:
  1. 25,872 cm3
  2. 38,808 cm3
  3. 12,936 cm3
  4. 1,848 cm3
8.
Assertion (A): The curved surface area of a cone with radius 56 cm and slant height 70 cm is 12,320 cm2 (π = 22/7).
Reason (R): The curved surface area of a cone is πr2h.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Find the total surface area of a cone with radius 14 cm and slant height 50 cm (π = 22/7).
10.
Find the volume of a hemisphere of radius 42 cm (π = 22/7).
11.
The surface area of a sphere is 39,424 cm2 (π = 22/7). Find its radius.
12.
Find the volume of a cone with diameter 70 cm and height 12 cm (π = 22/7).
13.
Two spheres have radii in the ratio 7 : 9. Find the ratio of their volumes.
14.
A cone of radius 14 cm has a volume of 1,848 cm3 (π = 22/7). Find its height.
15.
A hemispherical bowl has an inner radius of 84 cm. How many litres of juice can it hold (π = 22/7)?
16.
Find the curved surface area of a cone with base diameter 140 cm and slant height 74 cm (π = 22/7).
Section C — Word problems4 × 4 = 16 marks
17.
A conical tent has a base radius of 7 m and a slant height of 12 m. Find the canvas needed and its cost at Rs 172 per m2 (π = 22/7).
18.
The dome of a building is a hemisphere of radius 35 m. Find the cost of painting its outer surface at Rs 38 per m2 (π = 22/7).
19.
An ice-cream cone has radius 7 cm and height 6 cm. How much ice-cream do 19 such cones hold (π = 22/7)?
20.
A metal sphere of radius 2 cm is melted and recast into cones of radius 1 cm and height 2 cm. How many cones are made?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Math of Space: Surface Area and Volume · AW-9M-SAV-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 50 cm√(142 + 482) = √2500 = 50
2(c) 2,200 cm2πrl = 22/7 × 14 × 50 = 2,200
3(d) 61,600 cm24πr2 = 4 × 22/7 × 702 = 61,600
4(c) 1,848 cm23πr2 = 3 × 22/7 × 142 = 1,848
5(c) πrlr = radius, l = slant height
6(a) 179,666 2/3 cm3(4/3)πr3 = 4/3 × 22/7 × 353 = 179,666 2/3
7(c) 12,936 cm3(1/3)πr2h = 1/3 × 22/7 × 212 × 28 = 12,936
8(c) A is true, but R is false.A is true: πrl = 22/7 × 56 × 70 = 12,320. R is false.
92,816 cm2πr(l + r) = 22/7 × 14 × 64 = 2,816
10155,232 cm3(2/3)πr3 = 2/3 × 22/7 × 423 = 155,232
1156 cm4 × 22/7 × r2 = 39,424, so r2 = 3136, r = 56
1215,400 cm3r = 35; (1/3) × 22/7 × 352 × 12 = 15,400
13343 : 729volume goes as r3: 73 : 93
149 cm(1/3) × 22/7 × 142 × h = 1,848, so h = 9
151241.856 litres(2/3) × 22/7 × 843 = 1,241,856 cm3 = 1241.856 litres
1616,280 cm2r = 70; πrl = 22/7 × 70 × 74 = 16,280
17264 m2; Rs 45,408πrl = 22/7 × 7 × 12 = 264 m2; × 172 = 45,408
18Rs 292,6002πr2 = 2 × 22/7 × 352 = 7,700 m2; × 38 = 292,600
195,852 cm3one cone = (1/3) × 22/7 × 49 × 6 = 308; × 19 = 5,852
2016 cones(4/3)π × 23 ÷ ((1/3)π × 12 × 2) = 4 × 8 ÷ 2 = 16