Advertisements
Advertisements
प्रश्न
The ratio of the total surface area of a sphere and a hemisphere of same radius is
पर्याय
2 : 1
3 : 2
4 : 1
4 : 3
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the total surface area of a hemisphere 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 area.
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r 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.
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.
The total surface area of a hemisphere of radius r is
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
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
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
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
The volume of a sphere is 905 1/7 cm3, find its diameter.
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
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`)
