Class 10 Conversion of Solids — practice questions with answers

Mensuration · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. When a solid is melted and recast into another shape, which quantity always stays the same?

AVolume
BSurface area
CHeight
DRadius

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Answer: A) Volume

Melting and recasting conserves the amount of material, so the volume remains unchanged while shape and surface area may differ.

2. A metal cylinder of radius 3 cm and height 12 cm is melted. Its volume in terms of pi (cm³) is:

A108 pi
B36 pi
C72 pi
D144 pi

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Answer: A) 108 pi

V = pi*r²*h = pi*9*12 = 108 pi cm³.

3. A solid cone of radius 3 cm and height 9 cm is melted into a cylinder of height 9 cm. The radius of the cylinder is:

A $3$ cm
B3 cm
C9 cm
D1 cm

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Answer: A)

3

\frac{1}{3}

pi*3²*9 = pi*r²*9 =>

\frac{1}{3}

*9 = r² => r² = 3 => r =

3

cm.

4. A goldsmith in Jaipur melts a metal cuboid of dimensions 77 cm x 72 cm x 7 cm and casts it into a sphere.
Find the radius of the sphere (in cm). (use pi =

\frac{22}{7}

)

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Answer: D) 21

Cuboid V = 77*72*7 = 38808 cm³.

\frac{4}{3}

\frac{22}{7}

*r³ = 38808 =>

\frac{88}{21}

*r³ = 38808 => r³ =

\frac{38808 * 21}{88}

= 9261 => r =

39261

= 21 cm.

5. A solid metallic sphere of radius 'r' is melted and drawn into a long cylindrical wire of radius

\frac{r}{10}

.
The length of the wire, in terms of r, is:

A $\frac{400}{3}$ r
B $\frac{4}{3}$ r
C $\frac{40}{3}$ r
D $\frac{4000}{3}$ r

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Answer: A)

\frac{400}{3}

\frac{4}{3}

pi*r³ = pi*(

\frac{r}{10}

)²*L = pi*(

\frac{r ^{2}}{100}

)*L =>

\frac{4}{3}

r³ =

\frac{r ^{2} * L}{100}

=> L =

\frac{4}{3}

*100*r =

\frac{400}{3}

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