Question

A heap of water in the form of a cone whose diameter is 21cm and height is 6cm .find its volume. the heap is to be covered by canvas to protect it from rain. find the area of the canvas required​

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find volume of heap
• area of the canvas required to cover the heap

$\huge\bf\underline \purple{ \mathcal{S}olution:-}$

$\bf\underline{\red{Given:-}}$

• Diameter of heap = 21cm
• Radius = 10.5cm
• height of heap = 6cm

we know that,

$\red{ \bigstar \star} \green{ \bf \: Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h }$

$\rm \leadsto volume = \frac{1}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 6$

$\rm \leadsto volume = \frac{44}{7} \times 110.25$

$\rm \leadsto volume = {44} \times 15.75$

$\rm \leadsto volume = 693 {cm}^{3}$

Now,

$\underline{ \large \red{ \mathscr{A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

The heap is to be covered by canvas to protect it from rain.

$\red{ \bigstar \star} \green{ \bf \: CSA \: of \: cone = \pi {r}l }$

• Finding Slant height :-

⇝ l² = r² + h²

⇝ l² = 10.5 × 10.5 + 6 × 6

⇝ l² = 110.25 + 36

⇝ l² = 146.25

⇝ l = √146.25

⇝ l = 12.09

So,

⪼Area of the canvas = 22/7 × 10.5 × 12.09

⪼ Area of the canvas = 22/7 × 126.945

⪼ Area of the canvas = 398.97 cm²

Hence,

• Area of canvas required = 398.97cm²

• Volume of heap = 693cm³

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