Question

5. A bucket is in the form of a frustum of a cone. its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. Find how much water can the bucket hold?

Answer 1

Given :-

A bucket is in the form of a frustum of a cone. its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively.

To Find :-

Water can the bucket hold

Solution :-

Radius of frustum = Diameter/2

Radius = 56/2

Radius = 28 cm

Now

Radius = 42/2

Radius = 21 cm

Now

We know that

Volume of frustum = 1/3 × πh [(r² + r'²) + r × r']

Volume = 1/3 × 22/7 × 15[(28² + 21²) + 28 × 21]

Volume = 22/21 × 15[(784 + 441) + 588]

Volume = 22/7 × 5[1813]

Volume = 110/7 × 1813

Volume = 28490 cm³

Now

1 l = 1000 cm³

28490 cm³ = 28490/1000 = 28.49 L

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Answer 2

Solution :

$\setlength{\unitlength}{1cm}\begin{picture}\linethickness{0.4mm}\qbezier( - 1, 0)( - 1,0)(1,3)\qbezier(5.2, 0)(5.2,0)(3,3)\qbezier(1, 3)(2,2.5)(3,3)\qbezier(1, 3)(2,3.5)(3,3)\qbezier( - 1, 0)(1.8, 0.8)(5.2,0)\qbezier( - 1, 0)(1.8, - 1)(5.2,0)\qbezier(4.8, 0)( - 1, 0)(5.2,0)\qbezier(3, 3)(1, 3)(3,3)\put(2,0){\dashbox{0.2}(1,3)}\put(2,0){\circle*{0.19}}\put(2,2.99){\circle*{0.19}}\put(1.2,1.3){\bf 15 \: cm }\put(3.2,-1){\bf 28 \: cm }\put(2.3,3.4){\bf\ 21 \: cm }\end{picture}$

• A bucket is in the form of a frustum of a cone.

• Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively.

We need to find the capacity of the bucket .

Refer to the figure of the bucket above .

Radius of the upper portion > 28 cm

Radius of the lower portion > 21 cm .

Volume of the frustum of a cone -

> ⅓ πrh( r² + R² + rR )

> ⅓ π × 15( 1813)

> 1/3 × 22/7 × 15 × 1813

> 5 × 22 × 259

> 28490 cm³ .

Answer - The bucket can hold 28490 cm³ of water.

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