Spheres

Q. Water is dripping out from a conical funnel a uniform rate of 4 cm cube per second through a tiny hole at the vortex in the bottom when the slant height of the water is 3 cm find the rate of decrease of slant height of the water given that the Vertical angle of the funnel is 120 degree

Q. Lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are fully submerged. If the diameter of the beaker is 18 cm and water rises by 40 cm. find the number of lead spheres dropped in the water.

Q. 30. A cone of maximum volume is inscribed in a given sphere. Then show that the ratio of the height of the cone to the diameter of the sphere is ⅔.

Q. ntA parallel plate capacitor each plate of 0.06 m diameter and 0.05 cm of air what is the capacity of capacitor .what would be the radius of sphere having the same capacitamce .n

Q.

The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm is:

1. 2110 $c{m}^2$

2. 2310 $c{m}^2$

3. 1155 $c{m}^2$

4. 1055 $c{m}^2$

Q.

A cube is cut into x smaller cubes each of volume 8$c{m}^3$. If volume of the entire cube is 512 $c{m}^3$, then find the value of 'x'.

1. 16

2. 96

3. 64

4. 32

Q. 21 glass spheres, each of radius 2 cm are packed in a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and, then the box is filled with water. Find the volume of water filled in the box.

Q. A dome of building is in the form of a hemisphere, from inside it was white washed at the cost of Rs498.96 . If the cost of white washed is 2.00 per sq.mtr. Find (i) Inside surface area of the dome (ii) Volume of the air inside the dome

Q. The radius of sphere is increased by 12.5% , Prove that the volume is increased by 42.38% approximately.

Q. 45. A solid metallic right circular cone 20 cm high and vertical angle 60^° is cut into two parts at the middle point of its height by a plane parallel to the base . If the frustum so obtained be drawn into a wire of diameter 1/16 cm find length of wire

Q. 32. A semi-circular sheet of metal diameter 28cm is bent to form an open conical cup. Find the capacity of cup.

Q. A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?

Q.

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c{m}^3$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $\pi$ = $\frac{22}{7}$)

1. 10

2. 12

3. 14

4. 16

Q.

The area of one face of a cube is $100m^2$. Find the volume of the cube.

1. 3000 $m^3$

2. 2000 $m^3$

3. 1000 $m^3$

4. 500 $m^3$

Q. A metallic right circular cone 20 cm high and those vertical angle is 60^° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16cm, find the length of the wire

Q.

The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm is:

1. 1155 $c{m}^2$

2. 1055 $c{m}^2$

3. 2110 $c{m}^2$

4. 2310 $c{m}^2$

Q. Total surface area of a right circular cone
$=\pi r(r+l)$

1. False
2. True

Q. State True(1) or False(0).

Q.

Hanumappa and his wife Gangamma are busy making jaggery out of sugarcane juice. They have processed the sugarcane juice to make the molasses, which is poured into moulds in the shape of a frustum of a cone having the diameters of its two circular faces as 30 cm and 35 cm and the vertical height of the mould is 14 cm (see Fig.). If each $c{m}^3$ of molasses has a mass of about 1.2 g, find the mass of the molasses that can be poured into each mould( in kg). (Take $\pi$ = $\frac{22}{7}$)

1. 10

2. 12

3. 14

4. 16

Q.

Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

Q. Calculate the volume of a frustum cone given below: (Use $\pi$ = 3.14)

1. $113,829.168$ m${}^3$
2. $2873.10$ m${}^3$
3. $123,829.168$ in${}^3$
4. $133,829.168$ in${}^3$

Q.

Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

1. Sphere

2. Cone

3. Hemisphere

4. Cylinder

Q. Total surface area of a right circular cone
$=\pi r(r+l)$

1. True
2. False

Q. if the weight of a solid hemisphere is 6/5 that of a solid sphere of same material. the ratio of their radii will be

Q. Consider a frustum of cone with larger and smaller radius equal to $r_{1}and{r}_2$, respectively. Then, volume of frustum of a cone is $\frac{1}{3}\pi h(r_1^2+r_2^2+r_1{r}_2)$.

1. True
2. False
3. Insufficient Data
4. None of the above

Q. A cone is cut by a plane parallel to its base and the upper part is removed. The part that is left is called


(a) a cone
(b) a sphere
(c) a cylinder
(d) frustum of a cone

Q.

Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept.The name of the object/shape that exactly occupies this volume is

___.

Q.

The area of one face of a cube is $100m^2$. Find the volume of the cube.

1. 3000 $m^3$

2. 2000 $m^3$

3. 1000 $m^3$

4. 500 $m^3$

Q.

Match the following labels to their corresponding shapes.

$$\begin{array}{cc}\left(i\right)A& \left(a\right)Cylinder\\ \left(ii\right)B& \left(b\right)Frustum\\ \left(iii\right)C& \left(c\right)Cone\\ \left(iv\right)D& \left(d\right)Cuboid\end{array}$$

1. (i)-(b) , (ii)-(c) , (iii)-(d) , (iv)-(a)

2. (i)-(c) , (ii)-(b) , (iii)-(b) , (iv)-(d)

3. (i)-(c) , (ii)-(b) , (iii)-(b) , (iv)-(a)

4. (i)-(b) , (ii)-(c) , (iii)-(c) , (iv)- (d)

Q. An ellipse whose major axis is $2a$ and the minor axis is $2b$ revolves about the minor axis. The volume of the solid is equal to

1. $\frac{4}{3}\pi a{b}^2$
2. $\frac{2}{3}\pi a{b}^2$
3. $\frac{2}{3}\pi a^{2}b$
4. $\frac{4}{3}\pi a^{2}b$