Question

a circus tent is in the shape of a cylinder,upto a height of 8m.Surmounted by a cone of the same radius 28m.if the total height of the tent is 13m, findi() total inner curved surface area of the tent, ii) COST OF PAINTING INNER SURFACE AREA AT THE RATE OF rs 3.50m^2.

Answer 1

$\huge\sf\pink{Answer}$

i. 3910.72 ${m}^{2}$

ii. ₹ 13687.52

$\huge\sf\purple{Given :}$

Cylinder -

Height = 8 m

Radius = 28m

$\: \: \:$

Cone -

Height = (13 - 8)m

$\: \: \:\:\:\:\:\:\:\:\:\:\:$ = 5 m

Radius = 28 m

$\huge\sf\purple{To \:\:Find :}$

i. Inner Curved surface area of the tent

ii. Cost of painting inner curved surface area if the rate is ₹3.50 per ${m}^{2}$

$\huge\sf\purple{Formula \:\: used :}$

i. Curved Surface area of a cylinder = 2πrh

ii. Curved Surface area of a cone = πrl

$\huge\sf\purple{Solution :}$

Part 1 :

Curved surface area of a cylinder = 2πrh

$= 2 \times \frac{22}{7} \times 8 \times 28$

$= 2 \times 22 \times 8 \times 4$

$= 1408 \: {m}^{2}$

$\: \: \: \: \: \:$

Let, the latent height of the cone be l

${l}^{2} = {h}^{2} + {p}^{2}$

${l}^{2} = {5}^{2} + {28}^{2}$

${l}^{2} = 25 \: + \: 784$

${l}^{2} = 809$

$l \: = \sqrt{809}$

$l \: = 28.44 \: m\: \: (approx)$

$\: \: \: \:$

Curved Surface Area of the cone = πrl

$= \frac{22}{7} \times 28 \times 28.44$

$= 22 \times 4 \times 28.44$

$= 2502.72 \: m$

$\: \: \:$

Total Curved Surface Area = 2πrh + πrl

= (1408 + 2502.72) ${m}^{2}$

= 3910.72 ${m}^{2}$

$\: \: \:$

Part 2

Cost per ${m}^{2}$= ₹ 3.50

Cost of 3910.72 ${m}^{2}$= ₹ (3.50 × 3910.72)

= ₹ 13687.52

Answer 2

Answer:

Done

CSA OF CONE 2502.72

CSA OF CYLINDER 1408

TOTAL CSA 3910.72

COST PER M² 3.50 RUPPES

TOTAL COST 13687.52 RUPEES