Advertisements
Advertisements
Question
The ratio of the total surface area of a sphere and a hemisphere of same radius is
Options
2 : 1
3 : 2
4 : 1
4 : 3
Advertisements
Solution
In the given question,
The total surface area of a sphere (S1) = 4 \[\pi r^2\]
The total surface area of a hemisphere (S2) = 3 \[\pi r^2\]
So the ratio of the total surface area of a sphere and a hemisphere will be,
`S_1/S_2 = (4 pi r^2)/ (3 pi r^2)`
`= 4/3`
Therefore, the ratio of the surface areas is 4: 3 .
APPEARS IN
RELATED QUESTIONS
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
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`)
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Find the surface area of a sphere of radius 5.6 cm.
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
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.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
The total surface area of a hemisphere of radius r is
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
The ratio between the volume of a sphere and volume of a circumscribing right circular 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 and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
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.
Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
The total surface area of a hemisphere is how many times the square of its radius
