Question

The cylindrical end of a pencil is sharpened to produce a perfect cone at the end with no overall loss of length . If the diameter of the pencil is 1cm , and the cone is of length 2cm,calculate the volume of the shavings .​

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Answer 1

${ \huge{ \bold{ \underline{Given}}}}$

• Diameter of the pencil = 1cm

• The length of the cone is 2cm.

${ \huge{ \bold{ \underline{To \: find \: }}}}$

• Calculate the volume of the shavings.

${ \huge{ \bold{ \underline{ Solution:}}}}$

➥Radius of the pencil is 0.5cm.

➥Length of the conical portion( h) = 2cm

➥ Volume of the shavings will be the difference between end of pencil and cone

Therefore,

$➥{v}^ {shaving } \: = {v}^ {pencil } \: - \: {v}^ {cone }$

$➥ \frac{3\pi {r}^{2}h }{3} - \: \frac{\pi {r}^{2}h }{3}$

$➥ {\pi {r}^{2}h } - \: \frac{\pi {r}^{2}h }{3}$

$➥ \: \frac{2\pi {r}^{2}h }{3}$

$➥ \frac{2 \times \frac{22}{7} \times ( {0.5}^{2} ) \times 2}{3}$

$➥ \frac{88 \times 0.25}{7 \times 3}$

$➥ \frac{220}{21}$

$➥1.0472 \: {cm}^{3}$

➸Therefore the volume of the shavings = 1.0472 cubic units.

Answer 2

lthe intellectual and practical activity encompassing the systematic study of the structure and behaviour of the physical and natural world through observation and experiment.

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