Question

a cylindrical pillar is 50 cm in diameter and 3.5m in height.
find the cost of painting the csa of the pillar at the rate of rupees 15 per square metre

Answer 1

QUESTION:

a cylindrical pillar is 50 cm in diameter and 3.5m in height.

find the cost of painting the csa of the pillar at the rate of rupees 15 per square metre.

ANSWER:

FORMULA of curved surface area of cylinder

$2 \times \pi \times radius \times height$

cost of painting

$area \times rate \: of \: painting$

NOW COME TO YOUR QUESTION :

Diameter of cylindrical pillar = 50 cm.

Radius of cylindrical pillar will be =

$\frac{50cm}{2} \\ 25cm$

Height of pillar = 3.5 m.

Unit conversion :

$1m = 100cm$

$25cm = \frac{25}{100} m \\ \frac{1}{4} m$

rate of painting = 15/m^2.

curved surface area of cylinder :

$2 \times \frac{22}{7} \times \frac{1}{4} m \times \frac{35}{10} m \\ \\ \frac{11}{2} {m}^{2}$

cost of painting

$\frac{11}{2} {m}^{2} \times 15 {m}^{2} \\ ruppes\frac{165}{4}$

FINAL ANSWER :

RUPEES 165/4

Answer 2

Given :-

• Diameter = 50 cm

• Radius = d/2 = 50/2 = 25 cm

• Radius = 25/100 m = 0.25 m

• Height = 3.5 m

To find :-

• Cost of painting the CSA of the pillar at the rate of ₹ 15 per sq metre.

Solution :-

we know that,

$\orange{\bigstar}\:\:{\underline{\boxed{\bf\red{CSA\:of\:cylinder=2\pi{r}h}}}}$

According to the formula,

$\rm\longrightarrow\:CSA=2\pi{r}h$

$\rm\longrightarrow\:CSA=2\times\dfrac{22}{\cancel{7}}\times\:0.25\times\:\cancel{3.5}$

$\rm\longrightarrow\:CSA=2\times\:22\times\:0.25\times\:0.5$

$\rm\longrightarrow\:CSA=5.5\:{m}^{2}$

Now,

$\rm\:Cost\:of\:painting\:1{m}^{2}\:area=Rs\:15$

$\rm\:Cost\:of\:painting\: 5.5{m}^{2}\:area=Rs\:15\times\:5.5$

$\rm\:Cost\:of\:painting\: 5.5{m}^{2}\:area=Rs\:82.5$

Hence,the cost of painting the curved surface area of pillar at the rate of ₹15 per m² is ₹ 82.5.