Question

A container open at the top is in the form of a frustum of a cone of height 16cm with radii of its lower and upper ends as 8 cm 20 cm respectively .Find the cost of metal sheet used to make the container if it costs Rs.5 per 100cm square .(use pi= 3.14)

Answer 1

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Answer 2

Answer:

Total Cost of metal sheet is Rs. 98.05

Step-by-step explanation:

Given: Height of Frustum, h = 16 cm

          Upper radius of frustum, r = 20 cm

         Lower radius of frustum, R = 8 cm

To find : Cost of metal sheet used to make it.

Area of Metal sheet = Curved Surface Area of frustum + Area of Lower circle

slant height of frustum , l =  $\sqrt{h^2+(r-R)^2}=\sqrt{16^2+(20-8)^2}$

                                          =  $\sqrt{256+144}=\sqrt{400}=20\:cm$

Curved Surface Area of Frustum = $\pi l(r+R)$

                                                      = $\frac{22}{7}\times20\times(8+20)$

                                                      = $\frac{22}{7}\times20\times28$

                                                      = $22\times20\times4$

                                                      = 1760 cm²

Area of Lower/base circle = $\pi r^2=\frac{22}{7}\times(8)^2=201.14\:cm^2$

⇒ Area of Metal sheet = 1760 + 201.14 = 1961.14 cm ²

Cost of 100 cm² metal  = Rs. 5

Total cost of 1961.14 cm² metal = $\frac{5\times1961.14}{100}=Rs.\:98.05$

Therefore, Total Cost of metal sheet is Rs. 98.05