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CBSE Class 10  >  Class 10 Test  >  Mathematics (Maths)   >  Math Olympiad Test: Surface Area and Volume- 1 - Class 10 MCQ

Math Olympiad Test: Surface Area and Volume- 1 - Free MCQ with solutions


MCQ Practice Test & Solutions: Math Olympiad Test: Surface Area and Volume- 1 (10 Questions)

You can prepare effectively for Class 10 Mathematics (Maths) Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Surface Area and Volume- 1". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Surface Area and Volume- 1 - Question 1
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Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. What is the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm?

Detailed Solution: Question 1

Let the no. of marbles = x
Radius of marble = 1.4/2 = 0.7 cm
Radius of cylinder = 7/2 = 3.5 cm

⇒ x = 150

Math Olympiad Test: Surface Area and Volume- 1 - Question 2
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A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

Detailed Solution: Question 2

The volume of cone = Volume of metal in the sphere

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Math Olympiad Test: Surface Area and Volume- 1 - Question 3
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A solid cylinder has height 12 cm and diameter 10 cm. A conical cavity of same height and same diameter is hollowed out. What is the total surface area of the remaining solid?

Detailed Solution: Question 3

Total surface area of the remaining solid = curved surface area of the cylinder + curved surface area of the cone + area of upper base of the cylinder 
= 2πrh + πrl + πr2

Math Olympiad Test: Surface Area and Volume- 1 - Question 4
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The surface area of the cylinder is 2992 cm2 and its height is 20 cm, what is the diameter of the cylinder?

Detailed Solution: Question 4

Let r be the radius of the cylinder Total surface area = 2πr (h + r)

⇒ r2 + 20r - 476 = 0
⇒ r2 + 34r - 14r - 476 = 0
⇒ r(r + 34) - 14(r + 34) = 0
⇒ (r - 14) (r + 34) = 0
⇒ r = 14; r = -34 (Not possible)
diameter = 2 × 14 = 28 cm

Math Olympiad Test: Surface Area and Volume- 1 - Question 5
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The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. What is the height of the pillar?

Detailed Solution: Question 5

Curved surface area of cylindrical pillar = 264

From (1) and (2)

264r = 924 × 2

Math Olympiad Test: Surface Area and Volume- 1 - Question 6
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A solid iron hemisphere is melted and a number of solid iron balls of equal size are made. The radius of each ball is one-fourth the radius of the hemisphere. What are the number of balls that can be made?

Detailed Solution: Question 6

The radius of hemisphere = R
∴ Volume of hemisphere = 2/3 πR3
radius of spherical balls = R/4
Let the no. of spherical balls casted be x
∴ Volume of resulting spheres

Now,
Initial volume = Final volume,

Math Olympiad Test: Surface Area and Volume- 1 - Question 7
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A solid sphere of copper of radius 10.5 cm is melted and right cones of radius 3.5 cm and height 3 cm are made from the material. What is the number of cones made?

Detailed Solution: Question 7

Let the number of cones made be n. The volume of solid sphere = volume of resulting cones

Math Olympiad Test: Surface Area and Volume- 1 - Question 8
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The weight of a metallic spherical shell is 11.176 kg. If the inner radius of the cell is 6 cm. 1 cm3 of the metal weights 21 g then what is the thickness of the shell?

Detailed Solution: Question 8

Let the thickness of the shell be t
Inner radius = r, outer radius = R
∴ Volume of spherical shell = 4/3 π(R3 - r3)

∴ Weight of spherical shell

= 11.1786 kg
⇒ R3 = 343 ⇒ R = 7 cm
∴ Thickness = t = (R - r) = (7 - 6) = 1 cm

Math Olympiad Test: Surface Area and Volume- 1 - Question 9
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The ratio of the volumes of two spheres is 27 : 8. Find the ratio of their surface areas.

Detailed Solution: Question 9

Ratio of volumes of spheres of radii r1 and r2 respectively

Similarly,
ratio of surface areas

According to condition

∴ Ratio of surface areas

Math Olympiad Test: Surface Area and Volume- 1 - Question 10
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The surface area of a sphere is 616 cm2, what is the diameter of the sphere?

Detailed Solution: Question 10

Surface area of sphere = 4πr2 = 616

∴ diameter = 2r = 2 × 7 = 14 cm

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About this Class 10 Practice Test

This test contains 10 MCQs on Math Olympiad Test: Surface Area and Volume- 1 with detailed solutions for each question. It is part of the Mathematics (Maths) Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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