Tag: surface areas and volumes

Questions Related to surface areas and volumes

A solid sphere of radius $6\;cm$ is melted and recast into small spherical balls each of diameter $1.2\;cm$. Find the number of balls, thus obtained.

maths surface areas and volumes volume of a sphere problems involving volume of combined solids application of surface area and volume of solids

  1. $1000$.

  2. $1200$.

  3. $1100$.

  4. $100$.

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Correct Option: A
Explanation:

Number of balls $=$ $\dfrac { Volume\quad of\quad solid\quad sphere }{ Volume\quad of\quad 1\quad small\quad ball } $


                            $=$ $\dfrac { \dfrac { 4 }{ 3 } \pi { R }^{ 3 } }{ \dfrac { 4 }{ 3 } \pi { r }^{ 3 } } =\dfrac { 6\times 6\times 6 }{ 0.6\times 0.6\times 0.6 } $


                            $=$ $1000$

If the circumference of base of a hemisphere is $2\pi$ then its volume is _________ $cm^3$.

maths surface areas and volumes volume of a sphere problems involving volume of combined solids application of surface area and volume of solids

  1. $\dfrac{2\pi}{3}r^3$

  2. $\dfrac{2\pi}{3}$

  3. $\dfrac{8\pi}{3}$

  4. $\dfrac{\pi}{12}$

Show answer
Correct Option: B
Explanation:

The circumference of base of a hemisphere $=2\pi$
$\therefore 2\pi r=2 \pi$
$\therefore r=1$
Its volume $= \dfrac{2}{3}\pi (r)^3$
$= \dfrac{2}{3}\pi (1)^3 =\dfrac{2}{3}\pi$