A container, open at the top and made up of metal sheet, is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 14 cm respectively. Find the cost of metal sheet used to make the container, if it costs Rs 10 per 100 cm2.

Given: height of container frustum = h = 16 cm


Diameter of lower circular end = 16 cm


Diameter of upper circular end = 14 cm


Radius of lower circular end = r = 16/2 = 8 cm


Radius of upper circular end = R = 14/2 = 7 cm


Cost of 100 cm2 metal sheet = 10 Rs


Cost of 1 cm2 metal sheet = 10/100 = 0.1 Rs


Formula: Total surface area of frustum = πr2 + πR2 + π(R + r)l cm2


Where l = slant height




l = 16.0312 cm


Since the top is open we need to subtract the area of top/upper circle from total surface area of frustum because we don’t require a metal plate for top.


Radius of top/upper circle = R


Area of upper circle = πR2


area of metal sheet used = (total surface area of frustum)-πR2


= πr2 + πR2 + π(R + r)l- πR2 cm2


= πr2 + π(R + r)l cm2


= π × (82 + (7 + 8)16.0312) cm2


= 3.14 × 304.468 cm2


= 956.029 cm2


956.029 cm2 metal sheet is required to make the container.


Cost of 956.029 cm2 metal sheet = 956.029 × cost of 1 cm2 metal sheet


= 956.029 × 0.1 Rs


= 95.6029 Rs


Cost of metal sheet required to make container = 95.6029 Rs


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