A hemispherical dome, open at the base, is made from a sheet of fibre. If the radius of the hemispherical dome is 40cm and $\frac{13}{170}$ of the fibre sheet was wasted in making the dome, then find the cost of the dome at the rate of 35 per 100cm2 .

Chapter/Topic: surface areas and volume

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1234

2345

3808

3452

answer is C.

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Detailed Solution

the volume of the hemisphere.
⇒A= 2πr2=2×3.14×(40cm)2=10048 cm2 Assume that the area of fibre sheet used is equal to xx . As given that

\frac{13}{170}

of the fibre sheet was wasted in making the dome. So,
⇒10048 +

\frac{13}{170}

x = x
⇒10048 = x −

\frac{13}{170}

x
⇒10048 =

\frac{157}{170}

x
⇒x = 10048×

\frac{170}{157}

⇒x = 10880
The cost of fibre sheet for each 1cm2 =

\frac{35}{100}

rupees
The cost for 10880 cm2 =

\frac{35}{100}

×10880 = 3808 rupees.
Hence, Option (3) is the correct answer.

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