Question

2. A tent is made in the form of a conic frustum surrounded by a cone. The diameters of base and top
of the frustum are 14m and 7m and its height is 8m. The height of the tent is 12m. Find the area of

canvas. .(4m)​

Answer 1

Given:

A tent is made in the form of a conic frustum surmounted by a cone

The diameters of base and top  of the frustum are 14m and 7m and its height is 8m

The height of the tent = 12 m

To find:

The area of the canvas

Solution:

Let's assume,

h₂ = height of the frustum = 8 m

h₁ = height of the cone = 12 - 8 = 4 m

l₂ = slant height of the frustum

l₁ = slant height of the cone

R = radius of the base of the frustum = $\frac{14}{2}$ = 7 m

r = radius of the top of the frustum = radius of the base of the cone = $\frac{7}{2}$ = 3.5 m

We will find the slant heights of the frustum and the cone,

$l_1 = \sqrt{r^2 + h_1^2} = \sqrt{3.5^2 + 4^2} = \sqrt{12.25 + 16} = \sqrt{28.25} = 5.31\:m$

and

$l_2 = \sqrt{(R-r)^2 + h_2^2} = \sqrt{(7-3.5)^2 + 8^2} = \sqrt{3.5^2 + 8^2} = \sqrt{12.25 + 64} = \sqrt{76.25} = 8.73\:m$

Now,

The required area of the canvas to make the tent is given by,

= [Lateral surface area of the frustum] + [Lateral surface area of the cone]

= [$\pi(R + r)l_2$] + [$\pi r l_1$]

= $[\frac{22}{7}\times (7+3.5) \times 8.73] + [\frac{22}{7}\times 3.5 \times 5.31]$

= $[\frac{22}{7}\times 10.5 \times 8.73] + [\frac{22}{7}\times 3.5 \times 5.31]$

= $[288.09\:m^2] + [58.41\:m^2]$

= $\bold{346.5\:m^2}$

Thus, the area of the canvas is 346.5 m².

---------------------------------------------------------------------------------------

Also View:

A tent consists of a frustum of a cone capped by a cone. If the radii of the ends of the frustum be 13m and 7m , the height of the frustum be 8m and the slant height of the conical cap be 12m, find the canvas required for the tent

https://brainly.in/question/958916

A tent is made in the form of a frustum of a cone surmounted by another cone, The diameters of the base and the top of the frustum are 20m and 6m respectively, and the height is 24m, If the height of the tent is 28m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required?

https://brainly.in/question/2715653