Question

A tent is of the shape of a right circular cylinder upto a height of 3 metres and then becomes a right circular cone with a maximum height of 13.5 metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of £ 2 per square metre, if the radius of the base is 14 metres.​

Answer 1

$\huge\mathfrak\purple{Bonjour!!}$

$\huge\mathcal\pink{Solution:-}$

⛄ Answer:-

Cost of painting = £ 2068

❄ Step-by-step explanation:-

Let r metres be the radius of the base of the cylinder and h metres be its height. Then, r= 14 m and h= 3 m.

Now,

Curved surface area of the cylinder = 2πrh m²

= [ 2 × 22/7 × 14 × 3] m²

= 264 m²

Now,

Let r1 m be the radius of the base, h1 m be the height and l m be the slant height of the cone. Then, r1 = 14 m, h1= (13.5 - 3)m = 10.5 m.

Therefore,

l1 = √r1² + h1²

=> l1 = √14² + (10.5)² m

=> l1 = √196 + 110.25 m

=> l1 = √306.25 m

=> l1 = 17.5 m.

Therefore,

The CSA of the cone = πr1l1

= 22/7 × 14 × 17.5 m²

= 770 m²

So,

The total area which is to be painted = CSA of the cylinder + the CSA of the cone.

= (264 + 770) m²

= 1034 m².

→ Hence, the cost of painting = £ (1034 × 2)

= £ 2068.

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Answer 2

$\bold{Given}\begin{cases}\underline{\footnotesize\sf{\star\:\:Dimensions\:of\:the\:Figure}}\\\sf{Height\:Total=13.5m}\\\sf{Radius(r)=14m}\\\sf{Height(h)\:of\:cylinder=3m}\\ \sf{\footnotesize\sf{Find\:cost\:of\:Painting\:inner\:tent\:@2/m^{2}}}\end{cases}$

Formula used :----

• CSA of cone = π × r × l
• slant Height(l) of cone = √(r²+h²)
• Height of cone = Total height - Height of cylinder.
• CSA of cylinder = 2πrh

${\large\bf{\mid{\overline{\underline{Solution:-}}}\mid}}$

Height of cone = 13.5 - 3 = 10.5m

Radius of cone = 14m

Slant Height of cone =

→ √[(10.5)² + (14)²]

→ √(110.25+196)

→√(306.25)

→ 17.5m

CSA of cone = 22/7 × 14 × 17.5 = 770m²

Now,

CSA of cylinder = 2 × 22/7 × 14 × 3 = 264m²

Total Area to be painted = CSA of both = 770+264 = 1034m²

Now, it is given that , cost of painting is $2 per m² .

so,

Total cost = 1034×2 = $2068 (Ans)

(Hope it helps you)