Question

A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom . find the volume of water left in the cylinder,if the radius of the cylinder is 60 cm and it height is 180cm .




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Answer 1

Answer:

Correct option is B)

Given, Radius of cone=60cm

Height of cone=120cm

Radius of hemisphere=60cm

Radius of cylinder=60cm

Height of cylinder=180cm

Volume of cone is,

=31πr2h

=31π×6602×120

=14000πcm3

Volume of hemisphere is,

=34πr3h

=32π603h

=144000πcm3

Volume of cylinder is,

=πr2h

=π×602×180

=648000πcm3

Volume of water left in cylinder is

=πr2h−31πr2h−34πr3h

=(648000−288000)π

=360000π

=1130400cm3

Answer 2

$\huge{\underbrace{\red{\bf{Solution}}}}$

♠️Given:

• Radius of cone = 60cm
• Height of cone = 120cm

Also,

• Radius of the hemisphere = 60cm

And,

• Radius of cylinder = 60cm
• Height of cylinder = 180cm

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♠️Answer:

=> Volume of cone = $\frac{1}{3}\pi \: r ^{2}$

=> $\frac{1}{3}\pi \times 660^{2} \times 120$

=> $\underline{\underline{\red{144000πcm³}}}$

=> Volume of hemisphere = $πr²h$

=> $\pi \times {60}^{2} \times 180$

=> $\underline{\underline{\pink{648000πcm³}}}$

Volume of water left in cylinder:

=> $(648000 - 288000)\pi$

=> $360000π$

=> $\underline{\underline{\green{1130400cm³}}}$ (Ans)

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