Question

A hemispherical dome of a mosque in Delhi needs to be painted. If the circumference of the base of the dome is 17.6 m , find the cost of painting it, given the cost of painting is rupees 50 per sq.m

Answer 1

AnswEr :

$\bold{Given}\begin{cases}\sf{Circumference \:of \: Base=17.6 m}\\ \sf{Cost \:of \:Painting=50@ {m}^{2} }\end{cases}$

• Let's Head to the Question Now :

$\longrightarrow \tt Circumference = 2\pi r$

$\longrightarrow \tt 17.6 = 2 \times \dfrac{22}{7} \times r$

$\longrightarrow \tt \cancel{17.6} \times \dfrac{7}{\cancel{22 \times 2}} = r$

$\longrightarrow \tt 0.4 \times 7 =r$

$\longrightarrow \red{\tt r = 2.8m}$

$\rule{300}{1}$

As the Top of Dome will only be Painted that's why we will find Curved Surface Area.

$\implies \tt Cost = CSA_{ \tiny \:Hemisphere} \times Rate \\\\ \implies \tt Cost =2\pi {r}^{2}\times Rate \\\\ \implies \tt Cost =2 \times \dfrac{22}{7}\times {(2.8)}^{2} \times 50 \\\\ \implies \tt Cost =100 \times \dfrac{22}{\cancel7}\times \cancel{7.84}\\\\ \implies \tt Cost =100 \times22 \times 1.12 \\\\\implies\large\boxed{\tt Cost =Rs. 2464}$

⠀

∴ Cost of Painting of Dome is Rs. 2464

Answer 2

Answer:

Step-by-step explanation:

Given :-

Circumference of the base = 17.6 m

To Find :-

Curved surface area of the hemisphere.

Total cost of painting.

Formula to be used :-

Circumference of circle = 2πr

Curved surface area of the hemisphere = 2πr²

Solution :-

Putting all the values, we get

Circumference of circle = 2πr

$\sf\implies 17.6 = 2 \times \dfrac{22}{7} \times\ r$

$\sf\implies44r= 17.6\times7$

$\sf\implies r = \dfrac{123.2}{44}$

$\bf\implies Radius = 2.8 \: m$

Now, Curved surface area of the hemisphere = 2πr²

$\sf\implies CSA=2\times\dfrac{22}{7}\times2.8^2$

$\bf\implies CSA=49.28 \: m^2$

Total cost of painting = ₹ 50 per m²

Total cost of painting = ₹ (50 × 49.28)

Total cost of painting = ₹ 2464