Advertisements
Advertisements
Question
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
Advertisements
Solution
According to the condition in the question,
`77 xx 16 = 1/3 pir^2h`
`=> 77 xx 16 = 1/3 xx 22/7 xx 7 xx 7 xx h`
`=> h = (77 xx 16 xx 3 xx 7)/(22 xx 7 xx 7)`
`=> h = (11 xx 16 xx 3)/22`
`=>` h = 24 m
We know that,
l2 = r2 + h2
`=>` l2 = (7)2 + (24)2
`=>` l2 = 49 + 576
`=>` l2 = 625
`=>` l = 25 m
∴ Curved Surface Area = πrl
= `22/7 xx 7 xx 25`
= 550 m2
Therefore the height of the tent is 24 m and it curved surface area is 550 m2.
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
