Question

The tent of height 8.25 m is in the form of a right circular cylinder with diameter 30 m and height 5.5 m surrounded by a right circular cone of same base find the cost of canvas of the tent at the rate of 45 rupees per metre square

Answer 1

The cost of canvas of the tent at the rate of 45 rupees = 122,505.52 Rs.

Step-by-step explanation:

Given:

The height of tent for right circular cylinder, h = 5.5 m,

The Base diameter of Cylinder,d = 30 m,

the base radius of Cylinder, r = 15 m,

The height of the conical tent can be found as:

The height of the conical tent = 8.25 - 5.5= 2.75 m

Now we can calculate the total surface area of the tent as:

$\textrm{Total surface area of Tent } =\textrm{ Surface area of Cylindrical tent+ surface area of conical tent}\\\textrm{Total surface area of Tent } = (\pi r^2+2\pi r h) + (\pi r^2 + \pi r l)\\\textrm{Total surface area of Tent } = (\pi\ r^2+2\pi r h) + (\pi r^2 + \pi r l)$slant height of cone, l = $\sqrt{15^2+2.75^2}$ = 16.77m

So the total surface area of tent = $\textrm{Total surface area of Tent } = (\pi\ r^2+2\pi r h) + (\pi r^2 + \pi r l)\\\textrm{Total surface area of Tent } = (\pi\ 15^2+2\pi \times15 \times 5.5) + (\pi 15^2 + \pi\times 15 \times 16.77)\\\\\textrm{Total surface area of Tent } = 1225.22+1497.12\\\textrm{Total surface area of Tent } = 2722.34 m^2$

Now we can calculate the total cost of canvas to be used in tent = $45 \times 2722.34$

the cost of canvas of the tent at the rate of 45 rupees = 122505.52 Rs.

Answer 2

The cost of canvas is Rs. 55,687.5

Height of the tent = 8.25 m (Given)

Height of cylindrical = 5.5 m (Given)

Diameter of the cylinder = 30 m (Given)

Thus, Radius of the cylinder , r = 30 / 2  = 15 m

Let cone's slant height be = l

Therefore,

Height of the right circular cone -

= 8.25 - 5.5

= 2.75 m

Now,

l = √r² + h²

l = √(15)² + (2.75)²

l = √225 + 7.5625

l = 15.25

Total curved surface area of tent = Curved surface area of cylinder + Curved surface area of cone

= 2πrh + πrl

= πr(2h + l)

= π ×15 × (2 × 5.5 + 15.25)

= π × 15(11 + 15.25)

= 22/7 × 15 × 26.25

= 1,237.5

Therefore, the total curved surface area of the tent = 1,237.5 m²

Rate of canvas = Rs. 45 per m²

Cost of canvas of tent

= 1,237.5 m²  × 45

=  55,687.5

Therefore, the cost of canvas is Rs. 55,687.5