Tag: surface area and volume of sphere

Quizzes (0) Questions (33)

Questions Related to surface area and volume of sphere

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

Consider an incomplete pyramid of balls on a square base having $18$ players, and having $13$ balls on each side of the top layer. Then the total number $N$ of balls in that pyramid satisfies 

  1. $ 9000 < N <10000$
  2. $8000 < N < 9000$
  3. $7000 < N < 8000$
  4. $ 10000 < N < 12000 $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Top layer has $(13 \times 13)$ balls 
Similarly one layer below top layer will have $(14 \times 14) $ balls and we have $18$ lesens to total number of ball 
$ N = (13)^2 + (14)^2 + . . . . + (30)^2 $

$\displaystyle N = \frac {30 \times 31 \times 61} {6} = \frac {12 \times 13 \times 25} {6}$

$ N = 8805 $

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

The circumference of a 1 cm thick pipe is 44 cm. The level of water that 7 cm of pipe can hold is

  1. $798 cm^3$
  2. $308 cm^3$
  3. $792 cm^3$
  4. $795 cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given that

$2\pi r=44$
$r=7\ cm$

So, the inner radius of the pipe $=7-1=6\ cm$

Therefore, the volume of the pipe
$=\pi r^2h$
$=\pi \times 6^2\times 7$
$=792\ cm^3$

Hence, this is the answer.

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

The base of a right prism is a square of perimeter 20 cm and its height is 30 cm. The volume of the prism is

  1. $700 cm^3$
  2. $750 cm^3$
  3. $800 cm^3$
  4. $850 cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, perimeter $=4a=20$cm
$\therefore a=5$ cm
Area $=a^2=25  cm^2$
Volume $=$ Area $\times$ Height
Volume $=25 \times 30$
Volume $=750  cm^3$

Multiple choice maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

The base of a right prism is an equilateral triangle of edge $12$m. If the volume of the prism is $288\sqrt 3m^3$, then its height is:

  1. $6$m
  2. $8$m
  3. $10$m
  4. $12$m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

length of Equilateral triangle $= 12 m$
Area of equilateral triangle = $\displaystyle \frac{\sqrt{3}}{4}a^2$ = $\displaystyle \frac{\sqrt{3}}{4}(12)^2$ = $36\sqrt{3}$
Volume of prism = $288\sqrt{3} m^3$ = Area of triangle X height
$288\sqrt{3} m^3$ = $36 \sqrt{3} \times$ height
$\therefore $ Height $= 8 m$

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

If the circumference of the inner edge of a hemispherical bowl is $\displaystyle\frac{132}{7}:cm$, then what is the capacity?

  1. $12\pi\:cm^3$
  2. $18\pi\:cm^3$
  3. $24\pi\:cm^3$
  4. $36\pi\:cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\displaystyle2\pi r=\frac{132}{7}\implies r=3$

$\therefore$ Capacity $\displaystyle=\frac{2}{3}\pi r^3=18\pi$

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

The side of a cube is equal to diameter of the sphere. The ratio of volumes 
of cube and sphere is

  1. $\frac{11}{12}$
  2. $\frac{22}{11}$
  3. $\frac{11}{21}$
  4. $\frac{21}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the sides of cube be $s$ and radius of sphere be $r$

then $s=2r=(2r)^3=8r^3$
Volume of a cube$=s^3$
Volume of a sphere$=\cfrac{4}{3}\pi r^3$
Ratio of volume of cube and sphere$=\cfrac{8r^3}{\cfrac{4}{3}\pi r^3}$
$=\cfrac{8r^3}{\cfrac{4}{3}\times \cfrac{22}{7} r^3}\=\cfrac{21}{11}$

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

A hollow spherical shell is made of metal of density $4.8$ g/cm$^3$. If its internal and external radii are $10$ cm and $12$ cm respectively, find the weight of the shell

  1. $15.24 $ kg
  2. $12.84 $ kg
  3. $14.64 $ kg

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of spherical shell
$= \displaystyle \frac{4 \pi}{3} (R^3 - r^3) = \frac{4 \pi}{3} (12^3 - 10^3)$
$=\displaystyle \frac{4}{3} \times \pi \times (12 -10) (12^2 +12 \times 10 +10^2)$
$=\displaystyle \frac{4}{3} \times \pi \times 2 \times 264 cm^3$
$Weight = volume \times density = \displaystyle \frac{4}{3}\times \pi \times 364 \times 4.8 = 14.64 kg$

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

The radius of a sphere is r and radius of base of a cylinder is r and height is 2r. The ratio of their volumes will be-

  1. $2:3$
  2. $3:4$
  3. $4:3$
  4. $3:2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,

The radius of the sphere $=r$

The radius of the cylinder $=r$

The height of the cylinder $=2r$

 

We know that the volume of the sphere

${{V} _{1}}=\dfrac{4}{3}\pi {{r}^{3}}$

 

We know that the volume of the cylinder

$ {{V} _{2}}=\pi {{r}^{2}}h $

$ {{V} _{2}}=\pi {{r}^{2}}\left( 2r \right) $

$ {{V} _{2}}=2\pi {{r}^{3}} $

 

Therefore, the required ratio

$ \dfrac{{{V} _{1}}}{{{V} _{2}}}=\dfrac{\dfrac{4}{3}\pi {{r}^{3}}}{2\pi {{r}^{3}}} $

$ \dfrac{{{V} _{1}}}{{{V} _{2}}}=\dfrac{2\pi {{r}^{3}}}{3\pi {{r}^{3}}} $

$ \dfrac{{{V} _{1}}}{{{V} _{2}}}=\dfrac{2}{3} $

$ {{V} _{1}}:{{V} _{2}}=2:3 $

 

Hence, this is the answer.

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

The volume of a spherical shell whose internal and external diameters are $8cm$ and $10cm$ respectively (in cubic cm) is:

  1. $\cfrac{122\pi}{3}$
  2. $\cfrac{244\pi}{3}$
  3. $212$
  4. $257$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, internal diameter $=8cm$ and external diameter $=10cm$
Volume of a hollow sphere of outer Radius R and inner radius r $ = \frac { 4 }{ 3 } \pi ({R}^{2} -{ r}^{ 3 }) $
Inner radius of the spherical shell $ = \frac {8}{2} = 4 cm $
Outer radius of the spherical shell $ = \frac {10}{2} = 5  cm $
Hence, volume of spherical shell $ = \frac { 4 }{ 3 } \times \pi \times ({5}^{3} - {4}^{3}) = \frac { 4 }{ 3 } \times \pi  \times 61 = \frac {244\pi}{3}  { cm }^{ 3 }  $

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

A metallic hemispherical bowl is $0.25\;cm$ thick. The inside radius of the bowl is $5\;cm$. Find the volume of steel used in making the bowl.

  1. $43.25\;cm^3$
  2. $41.27\;cm^3$
  3. $42.25\;cm^3$
  4. $40.25\;cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of speed used $=$ $\dfrac { 2 }{ 3 } \pi \left( { r } _{ 1 }^{ 3 }-{ r } _{ 2 }^{ 3 } \right) $

${ r } _{ 1 }=5+0.25=5.25cm$
${ r } _{ 2 }=5cm$
$\therefore \quad $ Volume $=$ $\dfrac { 2 }{ 3 } \times \dfrac { 22 }{ 7 } \times \left( { \left( 5.25 \right)  }^{ 3 }-{ \left( 5 \right)  }^{ 3 } \right) $

                       $= \dfrac { 44 }{ 21 } \times \left( 144.70-125 \right) $

                       $= 41.27$ ${ cm }^{ 3 }$