Question

two hemispherical domes are to be painted as shown in the figure if the circumferences of the base of the domes are 17.6 cm and 70.4cm respectively, then find the cost of the painting at rupees 10 per cm

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The cost of painting two hemispherical domes at Rs. 10 per square cm is Rs. 8377.6

Step-by-step explanation:

Given that, there are two hemispherical domes which are to be painted.

The circumferences of the base of the domes are 17.6 cm and 70.4 cm respectively.

We know that,

Base of the hemispherical dome is a circle.

So, Circumference of a circle = $2\pi r$, where 'r' is the radius of the circle.

Let  $r_{1}$ be the radius of first hemispherical dome

Circumference of the first hemispherical dome = 17.6 cm

$2\pi r_{1}$ = 17.6

$r_{1}$ = $\frac{17.6 }{2\pi }$

$r_{1}$ = 2.8 cm.

Let  $r_{2}$ be the radius of second hemispherical dome

Circumference of the second hemispherical dome = 70.4 cm

$2\pi r_{2}$ = 70.4

$r_{2}$ = $\frac{70.4 }{2\pi }$

$r_{2}$ = 11.2 cm.

Curved surface area of hemispherical dome = $2\pi r^{2}$

Curved surface area of two hemispherical domes = $2\pi r_{1} ^{2} + 2\pi r_{2} ^{2}$

= (2 × $\pi$) [ $r_{1} ^{2} + r_{2} ^{2}$ ]

= $( \frac{44 }{7} )$ $[(2.8)^{2} +(11.2)^{2} ]$

= $( \frac{44 }{7} )$ $(133.28)$

= 837.76 $cm^{2}$

Given that, Cost of painting per square cm = Rs. 10

Cost of painting two hemispherical domes = Cost of painting 837.76 $cm^{2}$

= Rs. 10 × 837.76

= Rs. 8377.6

Therefore, the cost of painting two hemispherical domes is Rs. 8377.6

To know more about hemispherical domes, visit the links below:

https://brainly.in/question/48007524

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