Volume of Mixed Solids

Q. Question 14
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 and volume of the rocket [Use $\pi =3.14]$

Q.

A circus tent consists of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40m. The total height of the tent is 65m and that of the height of the cone is 30m. Find the volume of the tent and the area of the cloth used for making it.

1. $5658.63m^3,13835.57m^2$
2. $5325.42m^3,14251.57m^2$
3. $6354.36m^3,13921.46m^2$
4. $5657.14m^3,13828.57m^2$

Q. A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of $\frac{11}{3}$ $c{m}^3$ for each toy and all toys needs to be packed.(Take $\pi =\frac{22}{7}$)

1. 788

Q.

Question 9
An ice cream cone full of ice cream having radius 5 cm and height 10 cm as shown in figure. Calculate the volume of ice- cream, provided that its $\frac{1}{6}$part is left unfilled with ice – cream.

Q. Find the volume of the following figure in ($c{m}^3$)

Q.

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

1. 20

2. 30

3. 10

4. 25

Q. A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. Find the volume of the tent and the area of the cloth used for making it.

1. $5658.63m^3,13835.57m^2$
2. $5325.42m^3,14251.57m^2$
3. $226285.714m^3,15085.714m^2$
4. $5657.14m^3,13828.57m^2$

Q.

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the volume of the toy.

1. $10266.67c{m}^3$

2. $12266.67c{m}^3$

3. $17266.67c{m}^3$

4. $15266.67c{m}^3$

Q. Question 14
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 and volume of the rocket [Use $\pi =3.14]$

Q.

A metallic toy in the form of a cone of radius 11 cm and height 62 cm mounted on a hemisphere of the same radius is melted and recast into a solid cube. Find the surface area of the cube this formed.

Q. A girl fills a cylindrical bucket whose height is 32 cm and radius is 18 cm with sand. She empties the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24 cm, then find the slant height of the cone formed.

Q.

Find the Surface Area(in $c{m}^2$) of :

1. 900

2. 855.05

3. 820.75

4. 830.75

Q. A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. The volume of the tent is and the area of the cloth used for making it is .

1. $13828.57m^2$
2. $5657.14m^3$
3. $15085.714m^2$
4. $226285.714m^3$

Q.

Find the Surface Area(in $c{m}^2$) of :

1. 900

2. 855.05

3. 820.75

4. 830.75

Q.

Find the volume of the following figure in ($c{m}^3$ )

1. 18500

2. 19500

3. 20000

4. 20500

Q. A circus tent consist of a cylindrical base and a conical roof mounted on it. The radius of the cylinder is 40 m. The total height of the tent is 65 m and that of the cone is 30 m. The volume of the tent is and the area of the cloth used for making it is .

1. $13828.57m^2$
2. $5657.14m^3$
3. $15085.714m^2$
4. $226285.714m^3$

Q.

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. $[Take\pi =\mathrm{3.14.}]$

Q. A test tube has radius 2.1 cm and height 16.1 cm. Volume of the test tube is .

1. $324c{m}^3$
2. $213.4c{m}^3$
3. $516c{m}^3$
4. $981c{m}^3$

Q.

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the volume of the toy.

1. $10266.67c{m}^3$

2. $17266.67c{m}^3$

3. $15266.67c{m}^3$

4. $12266.67c{m}^3$

Q.

Shanta runs an industry in a shed which is in the shape of a cuboid surmounted by a half cylinder (see Fig.). If the base of the shed is of dimension 7 m × 15 m, and the height of the cuboidal portion is 8 m, find the volume of air that the shed can hold. Further, suppose the machinery in the shed occupies a total space of 300 $m^3$, and there are 20 workers, each of whom occupy about 0.08 $m^3$ space on an average. Then, how much air is in the shed (in $m^3$)? (Take $\pi =\frac{22}{7}$)

1. 827.15

2. 800

3. 845.3

4. 900

Q.

An ice cream ball of diameter $6\mathrm{cm}$. is placed over a cone of radius$2.5\mathrm{cm}$. and height $10\mathrm{cm}$.

Is the cone big enough to hold all the ice cream if it melts?

Q. Find the volume of the following triangular pyramid whose base is triangle with side of 18 cm and and altitude of 17 cm and height of pyramid is 23 cm?

Q.

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

Q. A solid uniform toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is $4.2cm$ and the total height of the toy is $10.2cm$, find the volume of the wooden toy.

Q. A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of $\frac{11}{3}$ $c{m}^3$ for each toy and all toys needs to be packed.(Take $\pi =\frac{22}{7}$)

1. 788

Q.

A toy in the shape of a hemisphere of radius 7cm is surmounted by a cone of slant height 25cm. The toy is placed in a cylindrical box of radius 70cm and height 1m, which is to be packed and dispatched. Find how many such toys can be accomodated in the box. Assume packaging occupies a volume of $\frac{11}{3}$ $c{m}^3$ for each toy and all toys needs to be packed.(Take $\pi =\frac{22}{7}$)

1. 700

2. 750

3. 769

4. 788

Q. Krishna runs an industry in a shed, which is in the shape of a cuboid surmounted by a half cylinder. If the base of the shed is of dimension 5 m × 15 m and the height of the cuboidal portion is 7 m, find the volume of the air that the shed can hold.
[Use 𝝅 = $\frac{22}{7}$]

Q.

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the volume of the toy.

1. $10266.67c{m}^3$

2. $17266.67c{m}^3$

3. $15266.67c{m}^3$

4. $12266.67c{m}^3$

Q. When we combine many solids to form one single solid, which of the following remains a constant?

1. Volume
2. Surface area
3. Perimeter
4. Curved Surface Area

Q.

What remains constant when solids are converted from one shape to another?

1. Coin base area + Coin C.S.A + Hemisphere C.S.A

2. Coin base area + Coin C.S.A + cone C.S.A

3. Total surface area of cone

4. Total surface area of coin + total surface area of cone