Surface area of a sphere

Q.

Find the radius of a sphere whose surface area is 154 cm².

Q.

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of their surface areas.

1. 1:5

2. 1:7

3. 1:9

4. 1:4

Q.

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Q.

The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motor cyclilst for riding.

Q.

The surface area of a sphere is $5544c{m}^2$. Find the diameter.

Q.

The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black Find the cost of paint required if silver paint costs 25 paise per $c{m}^2$ and black paint costs 5 paise per $c{m}^2$

Q.

Assuming the earth to be a sphere of radius 6370 km, how many square kilometres is area of the land, if three fourth of the earths surface is covered by water?

Q.

What is the diameter (in cm) of a sphere whose surface area is 616 $c{m}^2$?

1. 14 cm

2. 12 cm

3. 18 cm

4. 10 cm

Q.

A right circular cylinder just encloses a sphere of radius r. Find

Surface area of the sphere

Curved surface area of the cylinder

Ratio of the areas obtained above

Q.

If the radius of a sphere is tripled, what is the ratio of the volume of the original sphere to that of the second?

1. 1 : 9

2. 1 : 27

3. 1 : 3

4. 27 : 1

Q.

Find the surface area of a sphere of radius $14cm.$

Q.

Find the surface area of a sphere of diameter
(i) 14 cm (ii) 21 cm (iii) 3.5 cm

Q.

Find the radius of a sphere whose surface area is $154c{m}^2$

Q.

The surface area of a sphere of radius 7 cm is

1. 636 cm²

2. 616 cm²

3. 546 cm²

4. 702 cm²

Q.

The radii of two spheres are in ratio 1 : 2. Find the ratio of their surface areas.

Q.

Question 4
The radius of a spherical balloon increases from 7 cm to14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Q.

Find the surface area of a sphere whose volume is $606.375m^3$.

Q.

If the radius of a sphere is tripled, the ratio of the surface area of original sphere to that of the second is

1. 27 : 1

2. 1 : 9

3. 1 : 27

4. 9 : 1

Q. Question 2
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose and are to be painted silver.
Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black.
Find the cost of paint required if silver paint costs 25 paise $perc{m}^2$ and black paint costs 5 paise $perc{m}^2$.

Q. Question 3 (i)
A cloth having an area of $165m^2$ is shaped into the form of a conical tent of radius 5 m.

(i) How many students can sit in the tent, if a student on an average occupies $\frac{5}{7}{m}^2$ on the ground?

Q.

If radius of earth is approximately 4 times that of moon, then earth's surface area is 8 times that of moon.

1. True

2. False

Q.

Total surface area of a sphere is directly proportional to __ of radius of the sphere.

Q.

If the surface area of a sphere is 616 cm² its diameter is

1. 28 cm

2. 7 cm

3. 14 cm

4. 21 cm

Q.

In a circus, a motorcyclist performs stunts in a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is $14m,$ then find the area available for the motorcyclist to perform stunts. [Take $\pi =\frac{22}{7}$]

1. 616m²

2. 586m²

3. 486m²

4. 516m²

Q.

A cricket ball of radius $r$ fits exactly into a cylindrical tin as shown in the figure below. What will be the ratio between the surface areas of the cricket ball and the tin?

1. 2:3

2. 3:1

3. 3:5

4. 1:2

Q.

The total surface area of a hemispherical bowl of radius 77 cm is

1. 45602 cm²

2. 55900 cm²

3. 50002 cm²

4. 55902 cm²

Q.

If we take a circle and a sphere of the same radius, then the surface area of the sphere is ___ times the area of the circle.

Q.

If we take a circle and a hemisphere of the same radius, then the total surface area of the hemisphere is___ times the area of the circle.

Q.

Question 2 (iii)
Find the surface area of a sphere of diameter:

(iii) 3.5 m

$[Assume\pi =\frac{22}{7}]$

Q.

$\text{The volume of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm.The difference in their total surface areas is}\left(a\right)38c{m}^2\left(b\right)58c{m}^2\left(c\right)78c{m}^2\left(d\right)88c{m}^2$