Advertisements
Advertisements
प्रश्न
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
विकल्प
2r
3r
r
4r
Advertisements
उत्तर
In the given problem, we have a solid sphere which is remolded into a solid cone such that the radius of the sphere is equal to the height of the cone. We need to find the radius of the base of the cone.
Here, radius of the solid sphere (rs) = r cm
Height of the solid cone (h) = r cm
Let the radius of the base of cone (rc) = x cm
So, the volume of cone will be equal to the volume of the solid sphere.
Therefore, we get,
`(1/3) pi r_c^2 h = (4/3) pi r_s^3`
`(1/3) pi x^2 (r) = (4/3) pi (r)^3`
`x^2 = 4r^2`
` x = sqrt(4r^2)`
` x = 2r`
Therefore, radius of the base of the cone is 2r .
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 5.6 cm.
`["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 radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their surface areas.
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
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.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
The ratio of the total surface area of a sphere and a hemisphere of same radius is
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
Find the radius of the sphere whose surface area is equal to its volume .
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.
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?
