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

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• Diameter of heap is = 21cm

• Radius is = 10.5cm

• Height of heap is = 6cm

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the volume of heap?

• What's the area of the canvas required to cover the heap?

Formula to be used :-

• Volume of cone = ⅓πr²h

• CSA of cone = πrl

• l² = r² + h²

Where, l = Slant height

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

We know,

Volume of cone = ⅓ πr²h

Put the given values in the formula

Volume of cone

= ⅓ πr²h

= ⅓ × π × ( 10.5)² × 6

= 693 cm³

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Again, given that

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

To find CSA of cone, at first we need to find the slant height of the cone.

We know,

⟼ l² = r² + h²

⟼ l² = 10.5 × 10.5 + 6 × 6

⟼ l² = 110.25 + 36

⟼ l² = 146.25

⟼ l = √146.25

⟼ l = 12.09

• Slant height of cone = 12.09 cm

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Now, find CSA of cone

We know,

CSA of cone

= πrl

= 3.1416 × 10.5 × 12.09

= 398.97 cm²

Hence,

Volume of heap is = 693cm³

Area of canvas required = 398.97cm²

Answer 2

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