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Choose whether the given statement is true or false.

The volume of a solid in the form of a right circular cylinder with hemispherical ends whose length is 2.7 m and the diameter of each hemispherical end as 0.7 m is 0.9496 $m^{3}$ .

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True

False

answer is A.

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Detailed Solution

Given: Diameter of hemisphere = 0.7 m
Thus, its radius = 0.7/2 = 0.35 m
Now, height of cylinder = 2.7 – 0.35 – 0.35 = 2 m
We know that,
Volume of cylinder =

π r^{2} h

\frac{22}{7} \times {(0.35)}^{2} \times 2

= 22

\times 0.05 \times 0.35 \times 2

= 0.77

m^{3}

Now, volume of hemisphere =

\frac{2}{3} π r^{3}

\frac{2}{3} \times \frac{22}{7} \times {(0.35)}^{3}

\frac{2}{3} \times 22

\times 0.35 \times 0.05 \times 0.35

= 0.0898

m^{3}

Thus, volume of solid = volume of cylinder + 2

\times

volume of hemisphere
= 0.77 + + 2

\times 0.0898

= 0.9496

m^{3}

Hence, this is a true statement.

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