Tag: surface areas and volumes

Quizzes (11) Questions (22)

Questions Related to surface areas and volumes

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

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.

  1. $1000$.
  2. $1200$.
  3. $1100$.
  4. $100$.
Reveal answer Fill a bubble to check yourself
A Correct answer
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 } $


                            $=$ $1000$

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

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

  1. $\dfrac{2\pi}{3}r^3$
  2. $\dfrac{2\pi}{3}$
  3. $\dfrac{8\pi}{3}$
  4. $\dfrac{\pi}{12}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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