Question

1.|| A bucket open at the top, and made up of a metal sheet is in the form of frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs 10 per 100 m².

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Answer 1

Answer

• Cost of metal sheet = ₹ 171.13

Given

• A bucket open at the top, and made up of a metal sheet is in the form of frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively

To Find

• The cost of metal sheet used in it at the rate of Rs 10 per 100 cm²

Formula Used

Total Surface Area of Conical Frustum , TSA = πR² + πl(R+r) + πr²

Slant height , l = √[h²+(R-r)²]

Solution

Here the frustum is open .

So , TSA = πr² + πl (R+r)

Slant height , l = ? cm

Height  = depth , h = 24 cm

Upper diameter , D = 30 cm

⇒ Upper radius , R = 15 cm

Lower diameter , d = 10 cm

⇒ Lower radius , r = 5 cm

Now ,

$\tt l = \sqrt{h^2+(R-r)^2}\\\\\implies \tt l=\sqrt{24^2+(15-5)^2}\\\\\implies \tt l=\sqrt{576+100}\\\\\implies \tt l=\sqrt{676}\\\\\implies \tt l=26\;cm$

TSA of Conical Frustum ,

⇒ πr² + πl(R+r)

⇒ π(5²) + π (26)[15+5]

⇒ 25π + 520π

⇒ π (25+520)

⇒ 545π

⇒ 1711.3

So , TSA of Conical frustum = 1711.3 cm²

Cost of  100 cm² metal sheet = ₹ 10

⇒ Cost of 1 cm² metal sheet = ¹⁰/₁₀₀

⇒ Cost of 1 cm² metal sheet = ₹ 0.1

So ,

Cost of 1711.3 cm² metal sheet = 1711.1 × 0.1

⇒ Cost of metal sheet = ₹ 171.13

Answer 2

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