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A bucket made of metal sheet …

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A bucket made of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8cm 20cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs 15 per 100 cm×cm.
  • 1 answers

Sia ? 4 years, 8 months ago

R = 20 cm, r = 8 cm and h = 16 cm
{tex}\therefore l = \sqrt { h ^ { 2 } + ( R - r ) ^ { 2 } } = \sqrt { ( 16 ) ^ { 2 } + ( 20 - 8 ) ^ { 2 } }{/tex}
{tex}= \sqrt { 256 + 144 } \mathrm { cm } = 20 \mathrm { cm }{/tex}
Total surface area of container = {tex}\pi l(R + r) + \pi {r^2}{/tex}
= [3.14{tex}\times{/tex}20{tex}\times{/tex}(20 + 8) + 3.14 {tex}\times{/tex}8{tex}\times{/tex}8] cm2
= (3.14{tex}\times{/tex}20{tex}\times{/tex}28+3.14{tex}\times{/tex}8{tex}\times{/tex}8)cm2
= (1758.4 + 200.96) cm2
= 1959.36 cm2
Cost of metal sheet used = {tex}\operatorname { Rs } \left( 1959.36 \times \frac { 15 } { 100 } \right) = R s .293 .90{/tex}

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