Question

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of rs 25 per metre. [use π = 22 7 ]

Answer 1

$\textbf{\huge{ANSWER:}}$

$\sf{Given\:is\:That:}$

Width of the cloth = 5 m

Diameter of the conical tent = 14 m

Height of the conical tent = 24 m

Cost of the cloth per m = Rs. 25

Value of $\tt{\pi}$ = $\frac{22}{7}$

$\sf{Your\:Solution:}$

Radius = $\frac{Diameter}{2}$

Curved Surface Area of the conical tent ( C.S.A. ) will be = $\pi r l$

Length will be = $\sqrt{h^{2} + r^{2}}$
=》 $\sqrt{24^{2} + 7^{2}}$
=》 $\sqrt{625}$

=》 $\boxed{\tt{l = 25 m}}$

Thus, the C.S.A. becomes = $\pi \times7 \times25$

=》 $\frac{22}{7}\times 7\times25$

=》 22 × 25

=》 $\boxed{\tt{C.S.A. = 550 m^{2}}}$

Width of the cloth = 5 m

Area of the cloth, we found = 550 $m^{2}$

Then, the length of the cloth will be = $\frac{550}{5}$ m

=》 $\tt{110 m}$

Given cost of the cloth per m = Rs. 25

Cost for 110 m cloth = 110 × 25

=》 $\boxed{\boxed{\tt{Rs 2750}}}$

Answer 2

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of rs 25 per metre.

Answer : Rs.2750

Step by step explanation :

Given :

Width of the cloth : 5 m.

Diameter of conical tent : 14 m

Height : 24 m

Cost of cloth : Rs. 25 per metre.

We know that,

Diameter = 2 r

14 = 2 r

r = 7 m

Slant Height of cone =

$\tt{L = \sqrt{h {}^{2} + r {}^{2} }}$

$\tt{L = \sqrt{24 {}^{2} + 7 {}^{2} } }$

$\tt{L = \sqrt{576 + 49}}$

$\tt{L = \sqrt{625}}$

$\tt{L = 25 \: m}$

Thus, Slant Height= 25 m.

Let's find the Curved surface area of conical tent.

$\small{ \tt{Curved \: surface \: area = \pi \: r \: l}}$

$\tt{= \frac{22}{7} \times 7 \times 25}$

$\tt{= \frac{22}{ \cancel7} \times \cancel 7 \times 25}$

$\tt{= 22 \times 25}$

$\tt{ = 550 \: m {}^{2}}$

Now,

C.S.A of conical tent = 550 m^2.

Width of cloth = 5 m

Length =$\tt{\frac{C.S.A}{Width}}$

$\tt {= \frac{550}{5} = 110 \: m}$

Cost of the cloth is 25 Rs. per metre.

${ \small \tt{\therefore \: Cost \: of \:110 m \: cloth = 110 \times 25}}$

$\tt{{ = Rs.2750}}$

Thus, The cost of 110 cloth is Rs. 2750