Sphere

Q.

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

1. $63.75\%$

2. $43.95\%$

3. $73.75\%$

4. $43.75\%$

Q.

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

1. $32.46m{m}^3$.

2. $22.46m{m}^3$.

3. $62.46m{m}^3$.

4. $28.46m{m}^3$.

Q. If a lemon of radius r is divided into four identical parts, then what would be the total surface area of the four parts? (Given Area of a sphere = $4\pi r^2$)

1. 2$\pi r^2$
2. 4$\pi r^2$
3. 6$\pi r^2$
4. 8$\pi r^2$

Q. If the radius of a sphere is doubled, how many times does its volume become?

1. 2 times
2. 6 times
3. 4 times
4. 8 times

Q. If a cone is cut into half by a plane parallel to its base, we get ____ .

1. a frustum and a cone
2. two frustums
3. two cones
4. a cone and a cylinder

Q.

A solid metallic cylinder of radius $3.5\text{cm}$ and height $14\text{cm}$ is melted and recast into a number of small solid metallic balls, each of radius $\frac{7}{12}\text{cm}$. Find the number of balls so formed.

Q.

Three solid spheres of iron whose diameters are $\mathbf{2}\mathbf{}\mathbf{cm}\mathbf{,}\mathbf{}\mathbf{12}\mathbf{}\mathbf{cm}$ and $\mathbf{16}\mathbf{}\mathbf{cm}$ respectively, are melted to form a single solid sphere. Find the radius of the solid sphere.

Q. Question 20
Volumes of two spheres are in the ratio 64 : 27 , then the ratio of their surface area is
(A) 3 : 4
(B) 4 : 3
(C) 9 : 16
(D) 16 : 9

Q. If a cone is cut into half by a plane parallel to its base, we get ____ .

1. two cones
2. a cone and a cylinder
3. a frustum and a cone
4. two frustums

Q. A cone of radius 7 cm and height 28 cm is recast into following shapes. Pair the radius in each case.

1. 7 cm
2. 3.5 cm
3. 213 cm

Q.

Question 6
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Q. If a well of height 20 m and diameter 7 m is dug out and the sand extracted from it is used to make a cuboid platform of length 14 m, breadth 22 m, then what is the height of the platform?

1. 10 m
2. 1 m
3. 2.5 m
4. 3.5 m

Q.

Volume of two spheres are in ratio 64: 27. Find the ratio of their surface areas.

Q.

Question 7
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per $m^2$. (Note that the base of the tent will not be covered with canvas.)

Q. How many balls can be placed in the cylindrical tube if they fit exactly as shown in the figure. The inner curved surface area of the cylinder is $30.8m^2$ and the surface area of each ball is $61600c{m}^2$. (Use $=\frac{22}{7}$)

1. 3
2. 4
3. 5
4. 6

Q. Question 54

State whether the following statement is True or False.

The given shape is a cylinder.

Q. A tent is in the shape of a cylinder surmounted by a conical top of the same diameter. If the height and diameter of the cylindrical part are $2.1m$ and $3m$ respectively and the slant height of the conical part is $2.8m$, Then the cost of canvas needed to make the tent if the canvas is available at the rate of $₹500$/sq. metre is ₹_____.(Use $\pi =\frac{22}{7}$)

1. 14, 500
2. 16, 500
3. 18, 500
4. 12, 500

Q. what is the formula of total surface area of frustrum of a right circular cone?

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

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

Q. The base of a cone need not to be circular in shape.

1. True
2. False

Q. Assertion :If the radius of a sphere is doubled, the surface area becomes four times the original surface area. Reason: Surface area of a sphere is proportional to the square of the radius of sphere.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Match the correct expression for volume of the following 3D - shapes.

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

Q. There is a toy rocket in the shape shown below. The base radius of the cylinder = 1.5 cm. Base radius of the cone = 2.5 cm. The total surface area (in sq.cm) of the toy .

1. 82.5$\pi$
2. 70.00$\pi$
3. 90.5$\pi$

Q. Question 8
From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c{m}^2$.

Q.

A sphere of the radius $6\text{cm}$ is melted and made three spheres of radius $3\text{cm},4\text{cm},\text{and}r\text{cm}$ respectively, then the value of $r$ is ______ .

Q.

A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in Fig. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take $\pi =3.14$) [4 MARKS]

Q. Question 19
In a right circular cone, the cross – section made by a plane parallel to the base is a
(A) circle
(B) frustum of a cone
(C) sphere
(D) hemisphere

Q. A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the total surface area of the rocket [Use $\pi =3.14]$

Q.

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[Take\pi =22/7.]$