Advertisements
Advertisements
प्रश्न
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
Advertisements
उत्तर
Radius of sphere = 9 cm
Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 9 xx 9 xx 9`
= `3054.857 "cm"^3 = 30.55 xx 10^-4 "m"^3` .....(i)
Diameter of cylindrical wire = 2 mm
Therefore, radius = 1 mm = 0.001 m
Let length of wire be h
∴ Volume = `pir^2h`
= `22/7 xx 0.001 xx 0.001 xx h`
= `3.142h xx 10^-6` m3 ....................(ii)
From (i) and (ii)
⇒ `3.142 xx 10^-6h = 30.55 xx 10^-4`
⇒ `h = (30.55 xx 10^-4)/(3.142 xx 10^-6)`
⇒ h = 972m
Length of the wire = 972 m
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of diameter 3.5 m.
`["Assume "pi=22/7]`
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 14 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
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.
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
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 surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
