Sphere

Q.

If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is

1. $\frac{2}{3}\pi r^3$

2. $3\pi r^3$

3. $9\pi r^3$

4. $\frac{1}{3}\pi r^3$

Q.

If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then $3\pi V{h}^3-S^2{h}^2+9V^2$ is equal to

1. 4 $\pi$

2. 32 ${\pi }^2$

3. 8

4. 0

Q. Question 7
A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceed its height?

Q.

In a sphere, the number of faces is

1. 2

2. 3

3. 1

4. 4

Q.

The solids are similar. Find the surface area of the red solid.Round your answer to nearest tenth if neceassary.

Q.

The area of four walls of a room of height 5 m is 144 m². If the total surface area of the room is 244 m² then its length is

1. 10 m

2. 15 m

3. 9 m

4. 8 m

Q.

If the diameter of a sphere is decreased by $25\%$, then its curved surface area decreases by:

1. $44.25\%$

2. $43.50\%$

3. $43.75\%$

4. $75.43\%$

Q.

Question 3
In a right circular cone, height, radius and slant height need not always to be the sides of a right triangle.

Q. Mark the correct alternative in each of the following:

In a sphere the number of faces is

(a) 1

(b) 2

(c) 3

(d) 4

Q. Question 9
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be$6:\pi$.

Q. Question 3
The diameter of a sphere is decreased by $25\%$. By what percent does its curved surface area decrease?

Q.

The diameter of a sphere is decreased by $25\%$. By what percent does its curved surface area decrease?

Q. Which one of the following schemes of ordering closed packed sheets of equal sized spheres does not generate closed packed lattice? 1. ABCABC 2. ABACABAC 3. ABBAABBA 4. ABCBCABCBC

Q. Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the sphere, if the diameter of the smaller one is 5 cm.

Q.

A solid sphere with centre 'O' of certain radius fits exactly into a right circular cone as shown in the diagram given below. If the volume of the sphere is 4186.67 ${cm}^3$, find the total surface area of the cone. (Take $\pi$ = 3.14). It is known that slant height of the cone is two times the radius of the base of the cone and the ratio of AO to DO is 2:1.

​

1. 400$\pi$ ${cm}^2$

2. 500$\pi$ ${cm}^2$

3. 900$\pi$ ${cm}^2$

4. 600$\pi$ ${cm}^2$

Q. A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine ${\text{(in mm}}^3)$is needed to fill this capsule? $\text{(Assume}\pi =\frac{22}{7})$

Q. The ratio of the volume and surface area of a sphere of unit radius without considering units is

1. 4 : 3
2. 3 : 4
3. 1 : 3
4. 3 : 1

Q.

The radius of a sphere is increased by $\mathrm{P}\%$. Its surface area increases by

1. $\mathrm{P}\%$

2. ${\mathrm{P}}^2\%$

3. $\left(2\mathrm{P}+\frac{{\mathrm{P}}^2}{100}\right)\%$

4. $\frac{{\mathrm{P}}^2}{2}\%$

Q. The volume of a sphere is equal to ___ the volume of a cylinder of the same height and diameter.

1. two –third
2. one –third
3. 8 times
4. double

Q. If the height of a cone is 4 cm and radius is 3 cm, compute its lateral height?

1. 7 cm
2. 5 cm
3. 6 cm
4. 5.5 cm

Q. A cricket ball of radius r fits exactly into a cylindrical tin as shown below. A ratio between the surface areas of the cricket ball and the tin is

1. 2:3
2. 3:2
3. 1:2

Q. If the radius of a sphere is doubled, then what is the ratio of new to the old surface area?

1. $1:2$
2. $2:1$
3. $4:1$
4. $1:4$

Q.

If the diameter of a sphere is decreased by $25\%$, then its curved surface area decrease by

1. $44.25\%$

2. $43.50\%$

3. $43.75\%$

4. $75.43\%$

Q.

Question 9 (iii)
A right circular cylinder just encloses a sphere of radius r (see figure). Find:

(iii) the ratio of the areas obtained in (i) and (ii).

Q.

If the diameter of a sphere is decreased by $25\%$, then its curved surface area decreases by:

1. $44.25\%$

2. $43.50\%$

3. $43.75\%$

4. $75.43\%$

Q. The volumes of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm. What is the difference in their total surface areas?

1. $88c{m}^2$
2. $100c{m}^2$
3. $84c{m}^2$
4. $44c{m}^2$

Q.

If the diameter of a sphere is decreased by $25\%$, then its curved surface area decreases by:

1. $44.25\%$

2. $75.43\%$

3. $43.50\%$

4. $43.75\%$

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. 3:1

2. 1:2

3. 2:3

4. 3:5

Q.

If a sphere is inscribed in a cube, find the ratio of the volume of the cube to the volume of the sphere.

Q.

If the diameter of a sphere is decreased by $25\%$, then its curved surface area decreases by:

1. $44.25\%$

2. $43.50\%$

3. $43.75\%$

4. $75.43\%$