Question

the given figure represents a solid consisting of a cylinder surmounted by a cone at one end and hemisphere at the other.find the volume of the solid

Answer 1

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Radius of cone = radius of cylinder = radius of hemisphere = 3.5cm
height of cylinder = 6.5cm
height of cone = 12.8 - 6.5 = 6.3cm

Volume of Solid = Volume of cone + Volume of cylinder + Volume of hemisphere

=1/3πr^2h + πr^2h + 2/3πr^3

=πr^2(1/3h + h + 2/3r)

=22/7×3.5×3.5 (1/3×6.3 + 6.5 + 2/3×3.5)

=385/10 (21/10 + 65/10 + 23.33/10 )

=385/10 × 109.33/10

=42092.05/100

=420.92cm^3


Volume of Solid is 420.92 cm^3.
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Answer 2

vol of solid= vol of cone + vol of cylinder+vol of hemisphere
$= 1 \div 3\pi \times r {}^{2}h + \pi \times r {}^{2} h + 2 \div 3\pi \times r {}^{3}$
=1/3×22/7×7/2×7/2×63/10 + 22/7×7/2×7/2×65/10 + 2/3×22/7×7/2×7/2×7/2
= (11×7×21)÷20 + (11×7×65)÷20 + (11×7)÷3
=1617÷20 + 5005÷20 + 77÷3
=6622÷20 + 77÷3
=(19866+1540)÷60
= 21406÷60
=420.93

so the vol of solid is 420.93 cm²