Question

11
From a solid cylinder block of radius 3x and height 8x, a sphere of radius x cm is drilled out
Find the volume of the remaining block.​

Answer 1

Required Answer:

To find the volume of the remaining block, we can simply subtract the volume of the sphere from the volume of the cylinder$.$

GiveN:-

• Radius and height of the solid cylinder is 3x cm and 8x cm.
• Radius of solid sphere = x cm

To FinD:-

• Volume of remaining block?

Step-by-Step Explanation:-

Volume of the remaining block = Volume of the cylinder - Volume of the sphere.

Formula we have to use:

• Volume of cylinder = πr²h
• Volume of sphere = 4/3 πr³

Finding the volume:

= πr'²h - 4/3 πr³

= π(3x)²8x - 4/3 πx³

= π(72x³) - 4/3 πx³

= π(72x³ - 4/3x³)

= π(212/3 x³)

= 22/7 × 212/3 x³

= 222.1 x³ (approx.)

Hence:-

• The required volume of the remaining block is 222.1 x³ (Answer)

Answer 2

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${ \bold { \underline{\large{Given : - }}}} \:$

❍ Radius and height of cylinder block is ㅤ3x and 8x respectively.

❍ Radius of sphere which is drilled out ㅤfrom cylinder block is x cm.

${ \bold { \underline{\large{To\:Find : - }}}} \:$

❍ Volume of the remaining block.

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$\large\boxed{\boxed{\sf{So\:let's \:do\:it\:!!}}}$

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${\red\bigstar\: { \boxed{\large{\bold\green{Volume_{(Cylinder\:block)}\:\leadsto\:\pi r^2 h }}}}} \:$

Putting all values :-

we will not put the value of pi to make the calculation easy!

$\longmapsto$ $\sf{\pi\:\times\:(3x)^2\:\times\:8x}$

$\longmapsto$ $\bold{\pi\:\times\:9x^2\:\times\:8x}$

$\longmapsto$ $\boxed{\bold{\pi\:\times\:72x^3}}\:\bigstar\:\:\:\:\red\leadsto\:\red{(1)}$

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${\red\bigstar\: { \boxed{\large{\bold\green{Volume_{(Sphere\:which\:is\:drilled\:out!)}\:\leadsto\:\dfrac{4}{3}\pi r^3}}}}} \:$

Putting all values :-

Putting all values :- we will not put the value of pi to make the calculation easy!

$\longmapsto$ $\bold{\dfrac{4}{3}\:\pi \:\times\:(x)^3}$

$\longmapsto$ $\boxed{\bold{\pi\:\times\:\dfrac{4}{3}x^3}}\:\bigstar\:\:\:\:\red\leadsto\:\red{(2)}$

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To find the volume of remaining block we had to subtract (2) from (1) i.e we had to subtract volume of sphere from volume of cylinder.

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Subtracting (2) from (1) :-

$\longmapsto$ $\bold{(\pi\:\times\:72x^3)\:-\:\bigg(\pi\:\times\:\dfrac{4}{3}x^3\bigg)}$

Value of pi is equal in both . So, we will take pi common to make calculation easy.

$\longmapsto$ $\bold{\pi\bigg(72x^3\:-\:\dfrac{4}{3}x^3\bigg)}$

$\longmapsto$ $\bold{\pi\bigg(\dfrac{216x^3\:-\:4x^3}{3}\bigg)}$

$\longmapsto$ $\bold{\pi\bigg(\dfrac{212}{3}x^3\bigg)}$

Now we will put value of pi to complete our answer.

$\longmapsto$ $\bold{\bigg(\dfrac{22}{7}\bigg)\bigg(\dfrac{212}{3}x^3\bigg)}$

$\longmapsto$ $\bold{\dfrac{22}{7}\:\times\:\dfrac{212}{3}\:\times\:x^3}$

$\longmapsto$ $\bold{\dfrac{4664}{21}\:\times\:x^3}$

$\longmapsto$ $\bold{\cancel{\dfrac{4664}{21}}\:\times\:x^3}$

$\longmapsto$ $\bold{222.09\:\times\:x^3}$

$\longmapsto$ $\boxed{\bold{222.09x^3}}\:\bigstar$

$\boxed {\frak {\therefore \purple {Volume\:of\:the\:remaining\:block\:\leadsto\:222.09x^3}}}\:\pink\bigstar$

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