Chapter 12.7, Problem 21PPS

To determine

Tocalculate:slant height of tent

Answer to Problem 21PPS

Slant height is equal to $\frac{700}{11}feets$

Explanation of Solution

Given information: A rectangular piece of canvas with dimensions 50 feet by 60 feet is used to make a tent. Diameter of a cone is 30 feet.

Formula used:Surface area (curved) cone is $\pi rl$ where $r$ denotes radius and $l$ denotes slant height of the cone.

Calculation:

First find area of the rectangular piece.

A rectangular piece of canvas is 50 feet by 60 feet.

So,

Area of canvas $=$ length $\times$ breadth $=50\times 60=3000$ feets (i)

Now find Surface area (curved) conical tent.

Surface area (curved) conical tent $=$

  $\pi rl$

Here, $r$ denotes radius and $l$ denotes slant height of the cone.

Diameter of cone (d) $=30$ feets

Radius of conical tent $(r)=\frac{diameter}{2}$

  $=\frac{30}{2}=15$ feets

So,

Surface area (curved) conical tent $=\pi (15)l$ (ii)

As a rectangular piece of canvas is used to make a tent,

Surface area (curved) conical tent $=$ Area of a rectangular piece

From (i) and (ii),

  $3000=\pi (15)\left(l\right)$

Put $\pi =\frac{22}{7}$

  $\begin{array}{c}3000=\left(\frac{22}{7}\right)(15)\left(l\right)\\ l=\frac{3000\times 7}{22\times 15}\\ =\frac{700}{11}feet\end{array}$

So,

Slant height of the cone is equal to $\frac{700}{11}feets$