Tag: surface area and volume of sphere

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Questions Related to surface area and volume of sphere

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 spherical shell of internal and external diameters $8 cm$ and $12 cm$, respectively is melted and recast into the form of a cone of base diameter $8 cm$. The height of the cone is

  1. $114 cm$
  2. $76 cm$
  3. $38 cm$
  4. $19 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of a hollow sphere of outer Radius R and inner radius r $ =

\cfrac { 4 }{ 3 } \pi ({R}^{3} -{ r }^{ 3 }) $

Inner radius of the spherical shell $ = \cfrac {8}{2} = 4 cm $

Outer radius of the spherical shell $ = \cfrac {12}{2} = 6  cm $

Volume of a cone $ = \cfrac { 1 }{ 3 } \pi { r }^{ 2 }h $  where r is the

radius of the base of the cone and h is the height.
Radius of the cone $ = \cfrac{8}{2} = 4  cm $

Now, Volume of the hollow sphere $ = $ Volume of cone
$ => \cfrac { 4 }{ 3 } \pi ({6}^{3} -{ 4 }^{ 3 }) = \cfrac { 1 }{ 3 } \pi { 4 }^{ 2 }h $
$ => 4 \times(216-64) = 16h $
$ h = 38  cm $

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 the smaller circle is $2$ m and the radius of the larger circle is $10$ m. What is the volume of the of the spherical shell inscribed in the larger circle?

  1. $3153.17 \space\ m^3$
  2. $4153.17 \space\ m^3$
  3. $2153.17 \space\ m^3$
  4. $153.17 \space\ m^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$R = 10 m$$
$r  = 2 m$
Volume $=\cfrac{4}{3}\pi (R^3-r^3)$
$=\cfrac{4}{3}\pi (10^3-2^3)$

$=\cfrac{4}{3}\pi (1000-8)$
$=\cfrac{4}{3}\pi (992)$
$=\cfrac{3968 \pi}{3}$
$=1322.66\pi $
$=4153.17 \space\ m^3$

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

The radius of the smaller circle is 4 cm and the radius of the larger circle is 8 cm. Find the volume of the of the spherical shell inscribed in the larger circle.

  1. $1875.62 \space\ cm^3$
  2. $875.62 \space\ cm^3$
  3. $2875.62 \space\ cm^3$
  4. $3875.62 \space\ cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

R $= 8\ cm$
r  $= 4\ cm$
Volume = $\dfrac{4}{3}\pi (R^3-r^3)$


= $\dfrac{4}{3}\pi (8^3-4^3)$

= $\dfrac{4}{3}\pi (512-64)$

= $\dfrac{4}{3}\pi (448)$

= $\dfrac{1792 \pi}{3}$
= $1875.62 \space\  cm^3$

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

The inside radius of a spherical metal shell is $25$ cm and the thickness of the shell is $10$ cm. Calculate the volume of the material used in the shell to the nearest unit.

  1. $124,087 \space\ cm$
  2. $144,087 \space\ cm$
  3. $114,087 \space\ cm$
  4. $134,087 \space\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Thickness, $T = R - r$
$10 = R - 25$
$R = 35$ cm
$r  = 25$ cm
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
$=$ $\cfrac{4}{3}\pi (35^3-25^3)$
$=$ $\cfrac{4}{3}\pi (42875-15625)$
$=$ $\cfrac{4}{3}\pi (27250)$
$=$ $\cfrac{109000 \pi}{3}$
$=$ $114,087 \space\ cm$

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 spherical shell 5 m thick has an outer radius of 7 m. What is the volume of shell?

  1. $1202.53\space\ m$
  2. $1302.53\space\ m$
  3. $1402.53\space\ m$
  4. $1102.53\space\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Thickness, $T = R - r$
$5 = 7 - r$
$r = 7 - 5 = 2$ m
$R = 7$ m
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (7^3-2^3)$
= $\cfrac{4}{3}\pi (343-8)$
= $\cfrac{4}{3}\pi (335)$
= $\cfrac{1340 \pi}{3}$
= $1402.53\space\ m$

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

A hollow spherical shell has inner diameter $4$ cm and outer diameter $8$ cm. Determine the volume of the shell.

  1. $204.45 \space\ cm^3$
  2. $134.45 \space\ cm^3$
  3. $234.45 \space\ cm^3$
  4. $334.45 \space\ cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Outer radius, $R = 4$ cm
Inner radius, $r  = 2$ cm
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (4^3-2^3)$
= $\cfrac{4}{3}\pi (64-8)$
= $\cfrac{4}{3}\pi (56)$
= $\cfrac{224 \pi}{3}$
= $74.666\pi $
= $234.45 \space\ cm^3$

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 spherical shell has a outer radius $14$ m and inner radius $7$ m. What's the volume of the sphere?

  1. $\approx 9000 \space\ m^3$
  2. $\approx 8000 \space\ m^3$
  3. $\approx 10000 \space\ m^3$
  4. $\approx 7000 \space\ m^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Outer radius, $R = 14$ cm
Inner radius, $r  = 7$ cm
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (14^3-7^3)$
= $\cfrac{4}{3}\pi (2744-343)$
= $\cfrac{4}{3}\pi (2401)$
= $\cfrac{9604 \pi}{3}$
= $3201.33\pi $
$\approx 10000 \space\ m^3$

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

What is the volume of material that is needed to form a spherical shell whose outer radius is $5$ ft and whose inner radius is $3$ ft?

  1. $610.293 \space\ ft^3$
  2. $510.293 \space\ ft^3$
  3. $450.293 \space\ ft^3$
  4. $410.293 \space\ ft^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$R = 5$ ft
$r  = 3$ ft
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (5^3-3^3)$
= $\cfrac{4}{3}\pi (125-27)$
= $\cfrac{4}{3}\pi (98)$
= $\cfrac{392 \pi}{3}$
= $130.666\pi $
= $410.293 \space\ ft^3$

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

Calculate the volume of the material used in the shell to the nearest unit. The inside radius of a spherical metal shell is $2.5$ cm and the outer radius of the shell is $5$ cm.

  1. $257.91 \space\ cm^3$
  2. $457.91 \space\ cm^3$
  3. $417.91 \space\ cm^3$
  4. $357.91 \space\ cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$R = 5$ cm
$r  = 2.5$ cm
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (5^3-2.5^3)$
= $\cfrac{4}{3}\pi (125-15.625)$
= $\cfrac{4}{3}\pi (109.375)$
= $\cfrac{437.5 \pi}{3}$
= $1312.5\pi $
= $457.91 \space\ cm^3$

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

Determine the volume of a spherical shell which has an inner radius of $6$ cm and an outer radius of $24$ cm.

  1. $44972 \space\ cm^3$
  2. $56972 \space\ cm^3$
  3. $66972 \space\ cm^3$
  4. $56000 \space\ cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Outer radius, $R = 24$ cm
Inner radius, $r  = 6$ cm
Volume = $\cfrac{4}{3}\pi (R^3-r^3)$
= $\cfrac{4}{3}\pi (24^3-6^3)$
= $\cfrac{4}{3}\pi (13824-216)$
= $\cfrac{4}{3}\pi (13608)$
= $\cfrac{54432 \pi}{3}$
= $18144\pi $
= $56972 \space\ cm^3$