Verified answer

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 ,

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