Advertisements
Advertisements
Question
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
Options
1 : 4
1 : 3
2 : 3
2 : 1
Advertisements
Solution
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is 1 : 4.
Explanation:
Given that radius of a hemispherical balloon (r1) = 6 cm
Since, air is pumped into balloon.
Then, radius of hemispherical balloon (r2) = 12 cm
∴ Ratio of the surface areas of the balloon in both cases = `(3pir_1^2)/(3pir_2^2)`
`\implies r_1^2/r_2^2 = (6)^2/(12)^2`
= `36/144`
= `1/4`
= 1 : 4
Hence, ratio of the surface areas of the balloon in the two cases is 1 : 4.
APPEARS IN
RELATED QUESTIONS
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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.
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 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 dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
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.
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.
Find the radius of a sphere whose surface area is 154 cm2.
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, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes 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 volume of a sphere, if its surface area is 154 sq.cm.
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?
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`)
