Q. 174.7( 10 Votes )

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

Answer :

**Given:** Height of cylinder “h” = 3 m

Radius “r” = 14 m

Height of tent “H” = 13.5 m

Cost of painting = Rs 2 per m^{2}

**Formula Used:**

Curved surface area of cylinder = 2πrh

Curved surface area of cone = πrl

**Explanation:**

We have, r = 14 m

h = 3 m

CSA of cylinder = 2πrh

= 264 m^{2}

The height of the cone = Height of tent – height of cylinder

= 13.5 – 3

= 10.5 m

Now slant height of the cone is

Where r = 14 m and h = 10.5 m

⇒

⇒

⇒

⇒

We have shown, how to take square-root

⇒ l = 17.5 m

So CSA of cone = π r l

= 770 m^{2}

Total area to be painted = CSA of the cylinder + CSA of the cone

= 264 m^{2} + 770 m^{2}

= 1034 m^{2}

Cost of painting 1 m^{2} = Rs 2

Cost of painting 1034 m^{2} = Rs 2 × 1034

= Rs 2068

Hence cost of painting the tent is Rs 2068.

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