Advertisements
Advertisements
Question
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 .
Advertisements
Solution
Radius of cone = 15 cm
Height of cone = 36 cm
Curved surface of the cone = `pirl`
`l = sqrt(r^2 + h^2) = sqrt(15^2 + 36^2) = sqrt(1521) = 36`
Curved surface of cone = `22/7 xx 15 xx 39 = 1838.571` cm2
Curved surface of cone = Curved surface of sphere
⇒ `4pir^2 = 1838.571`
⇒ `4 xx 22/7 xx r^2 = 1838.571`
⇒ `r^2 = (1838.571 xx 7)/(4 xx 22)`
⇒ `r^2 = 146.25`
⇒ r = 12.09 cm
The radius of the sphere = 12.09 cm
RELATED QUESTIONS
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
`["Assume "pi = 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.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:
- maximum number of ball bearings that each box can have.
- mass of each box of ball bearings in kg.
(Use π = `22/7`)
