A hemispherical dome ,open at the base is made from a sheet from of fibre If the radius of - Maths - Surface Areas and Volumes

Question

A hemispherical dome ,open at the base is made from a sheet from
of fibre If the radius of the hemispherical dome is 40 cm and
13/170 part of the fibre is actually wasted in making the dome ,
find the cost of the dome at the rate of Rs 35 per 100
cm2 (use pi = 3 14)

Gursheen kaur. · Accepted Answer

Given: Radius of hemisphere =40cm

SA of hemisphere = $2 π r^{2} = 2 \times 3.14 \times {(40)}^{2} = 10048 {c m}^{2}$

Now,

Let the area of fibre sheet = x.....(i)

Also, 13/170 of fibre sheet actually used was wasted in making the dome, then

area of fibre sheet= $10048 + \frac{13}{170} x ..... (i i)$

∴From (i) & (ii), we get,

$10048 + \frac{13}{170} x = x \Rightarrow 10048 = x - \frac{13}{170} x \Rightarrow 10048 = (\frac{170 - 13}{170}) x \Rightarrow 10048 = (\frac{157}{170}) x o r x = 10048 \times \frac{170}{157} = 10880 {c m}^{2}$

Thus, the cost of dome at the rate of Rs. 35 per 100 ${c m}^{2}$ is

$= 10880 {c m}^{2} \times \frac{35}{100 {c m}^{2}} = R s . 3808$

A hemispherical dome ,open at the base is made from a sheet from of fibre. If the radius of the hemispherical dome is 40 cm and 13/170 part of the fibre is actually wasted in making the dome , find the cost of the dome at the rate of Rs. 35 per 100 cm2 (use pi = 3.14)

A hemispherical dome ,open at the base is made from a sheet from of fibre. If the radius of the hemispherical dome is 40 cm and 13/170 part of the fibre is actually wasted in making the dome , find the cost of the dome at the rate of Rs. 35 per 100 cm² (use pi = 3.14)