Q. 53.6( 12 Votes )

Answer :

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 cm^{2} metal sheet = 10 Rs

∴ Cost of 1 cm^{2} metal sheet = 10/100 = 0.1 Rs

Formula: Total surface area of frustum = πr^{2} + πR^{2} + π(R + r)l cm^{2}

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 = πR^{2}

∴ area of metal sheet used = (total surface area of frustum)-πR^{2}

= πr^{2} + πR^{2} + π(R + r)l- πR^{2} cm^{2}

= πr^{2} + π(R + r)l cm^{2}

= π × (8^{2} + (7 + 8)16.0312) cm^{2}

= 3.14 × 304.468 cm^{2}

= 956.029 cm^{2}

∴ 956.029 cm^{2} metal sheet is required to make the container.

∴ Cost of 956.029 cm^{2} metal sheet = 956.029 × cost of 1 cm^{2} 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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