Advertisements
Advertisements
प्रश्न
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
Advertisements
उत्तर
Side of square = 7 m
Radius of semicircle = `7/2` m
Length of the tunnel = 80 m
Area of cross-section of the front part = `a^2 + 1/2pir^2`
= `7 xx 7 + 1/2 xx 22/7 xx 7/2 xx 7/2`
= `49 + 77/4 m^2`
= `(196 + 77)/4`
= `273/4 m^2`
i. Therefore, volume of tunnel = area × length
= `273/4 xx 80`
= 5460 m3
ii. Circumference of the front of tunnel
= `2 xx 7 + 1/2 xx 2pir`
= `14 + 22/7 xx 7/2`
= 14 + 11
= 25 m
Therefore, surface area of the inner part of the tunnel
= 25 × 80
= 2000 m2
iii. Area of floor = l × b
= 7 × 80
= 560 m2
संबंधित प्रश्न
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
The ratio of the total surface area of a sphere and a hemisphere of same radius is
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
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 used.
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
