Mathematics Questions and Answers – Conversion of Solid from One Shape to Another

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Conversion of Solid from One Shape to Another”.

1. A metallic sphere whose radius is 5 cm is melted and cast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
a) 21.4 cm
b) 43.63 cm
c) 70 cm
d) 72.5 cm2
View Answer

Answer: b
Explanation: Volume of the sphere = volume of the cylinder
\(\frac {4}{3}\)πr3 = πr2h
\(\frac {4}{3}\) × 3.14 × 53 = 3.14 × 62 × h
h = \(\frac {4 \times 3.14 \times 3.14 \times 125}{3.14 \times 36}\)
h = 43.63 cm
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2. Three metallic spheres of radius 3 cm, 6 cm, 9 cm are melted into a single sphere. Find the radius of the resulting sphere.
a) 109.4 cm3
b) 4071.48 cm3
c) 1520 cm3
d) 1869.4 cm3
View Answer

Answer: b
Explanation: Volume of the resulting sphere = sum of the volumes of all three spheres
= \(\frac {4}{3}\)π33 + \(\frac {4}{3}\)π63 + \(\frac {4}{3}\)π93
= 113.09 + 904.77 + 3053.62
= 4071.48 cm3

3. A well of depth 25 m with a radius 4 m is dug from the earth forming a platform of length 28 m and a breadth of 16 m. Find the height of the platform.
a) 2.8 m3
b) 5 m3
c) 5.4 m3
d) 7.2 m3
View Answer

Answer: a
Explanation: Volume of the well = volume of the platform
πr2h = lbh
3.14 × 42 × 25 = 28 × 16 × h
h = 2.8 m3
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4. How many coins of 1 cm in diameter and thickness of 1.2 cm need to be melted to form a cuboid with dimensions of 5 cm × 10 cm × 4 cm?
a) 193
b) 213
c) 184
d) 282
View Answer

Answer: b
Explanation: Volume of the cuboid = number of coins(volume of a coin)
lbh = number of coins(πr2h)
5 × 10 × 4 = number of coins(3.14 × 0.52 × 1.2)
200 = number of coins(0.94)
number of coins = 213

5. A sphere of radius 14 cm is melted and cast into a number of tiny cones of radius 2.33 cm each and height 6 cm. Find the number of cones that will be formed?
a) 726
b) 816
c) 721
d) 821
View Answer

Answer: d
Explanation: Number of cones(volume of a cone) = volume of sphere
number of cones(\(\frac {1}{3}\)πr2h) = \(\frac {4}{3}\)πr3
number of cones(\(\frac {1}{3}\) × 3.14 × 2.332 × 6) = \(\frac {4}{3}\) × 3.14 × 143
number of cones(14) = 11488.21
number of cones = 821
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6. How many cylinders having 2.1 cm of radius and 1.4 cm of height can be made out of a cuboid metal box having dimensions 33 cm, 21 cm, 10.5 cm?
a) 152
b) 154
c) 844
d) 841
View Answer

Answer: c
Explanation: Number of cylinders(volume of a cylinder) = volume of a cuboid
Number of cylinders (πr2h) = lbh
Number of cylinders (3.14 × 1.42 × 1.4) = 33 × 21 × 10.5
Number of cylinders = 844

7. A sphere having a radius of 3 cm is melted and elongated into a wire having a circular cross-section of radius 0.1 cm. Find the length of the wire?
a) 2400 cm
b) 3100 cm
c) 1200 cm
d) 3600 cm
View Answer

Answer: d
Explanation: Volume of the wire = volume of the sphere
πr2h = \(\frac {4}{3}\)πr3
3.14 × 0.12 × h = \(\frac {4}{3}\) × 3.14 × 27
h = 3600 cm
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8. A cylindrical hole of depth 20 m with a radius 5 m is dug from the earth forming a platform of length 14 m and a breadth of 12 m. Find the height of the platform.
a) 8.34 m3
b) 11.84 m3
c) 7.64 m3
d) 9.34 m3
View Answer

Answer: d
Explanation: Volume of the cylindrical hole = volume of the platform
πr2h = lbh
3.14 × 52 × 20 = 14 × 12 × h
h = 9.34 m3

9. What is the formula to find the rise in the water level when ‘x’ spherical balls are dropped into a cylindrical beaker?
a) \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{Base \, area \, of \, cylinder}\)
b) \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{2(Base \, area \, of \, cylinder)}\)
c) The volume of the cylinder + volume of the beaker
d) The volume of the cylinder – 2(volume of the beaker)
View Answer

Answer: a
Explanation: To find the rise in the water level we require the volume of ‘x’ spherical balls and the base area of the cylinder
Rise in the water level = \(\frac {Volume \, of \, ‘x’ \, spherical \, balls}{Base \, area \, of \, cylinder}\)
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10. A metallic sphere whose radius is 4 cm is melted and cast into the shape of a right circular cone of radius 7 cm. Find the height of the cylinder?
a) 14.48 cm
b) 22.36 cm
c) 16.40 cm
d) 20.32 cm
View Answer

Answer: c
Explanation: Volume of the sphere = volume of the cone
\(\frac {4}{3}\) πr3 = \(\frac {1}{3}\) πr2h
\(\frac {4}{3}\) × 3.14 × 43 = 3.14 × 72 × h
h = \(\frac {4 \times 3.14 \times 3.14 \times 64}{3.14 \times 49}\)
h = 16.40 cm

11. Three metallic spheres of radius 2 cm, 4 cm, 8 cm are melted into a single sphere. Find the radius of the resulting sphere.
a) 1009.4 cm3
b) 2446.25 cm3
c) 1520 cm3
d) 2869.4 cm3
View Answer

Answer: b
Explanation: Volume of the resulting sphere = sum of the volumes of all three spheres
= \(\frac {4}{3}\)π23 + \(\frac {4}{3}\)π43 + \(\frac {4}{3}\)π83
= \(\frac {4}{3}\) × 3.14(23 + 43 + 83)
= 2446.25 cm3

Sanfoundry Global Education & Learning Series – Mathematics – Class 10.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter