Volume of Combination of solids

Q.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

1. 0.375

2. 0.875

3. 0.625

4. 0.125

Q. Question 7
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Q.

Selvi’s house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The overhead tank has its radius 60 cm and height 95 cm. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use $\pi$ = 3.14)

Q. Question 7
The curved surface area of a frustum of a cone is $\pi (r_1+r_2)l$, where $l=\sqrt{h^2+(r_1+r_2{)}^2}$ $r_{1}and{r}_2$ are the radii of the two ends of the frustum and h is the vertical height.

Q.

Question 8
Two solid cones A and B are placed in a cylindrical tube. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

Q.

Metallic spheres of radii 12cm, 8cm and 10cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

1. 12

2. 14.8

3. 18.5

4. 15.7

Q.

Question 6
Derive the formula for the curved surface area and total surface area of the frustum of cone.

Q.

Question 9
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Q. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 3. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article.
OR
A heap of rice is in the form of a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap ?

Q.

A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. [2 MARKS]

Q. Question 7
A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

Q.

Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is ___.

Q. The number of gold coins of 1.75 cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm is .

1. 400
2. 300
3. 200
4. 100

Q.

Find the area of copper sheet required to make a frustum shaped bucket of height 8 cm and radii 9 cm and 3 cm.

1. $129\pi c{m}^2$

2. $109c{m}^2$

3. $129c{m}^2$

4. $105c{m}^2$

Q. Question 2
The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Q.

Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere(in cm).

1. 12

2. 21

3. 18

4. 15

Q.

Question 13
A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

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

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

Q.

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c{m}^2$).

1. $56c{m}^2$

2. $40c{m}^2$

3. $52c{m}^2$

4. $48c{m}^2$

Q. A hemispherical bowl is made of brass, $0.25cm$ thickness. The inner radius of the bowl is $5cm$. Find the ratio of outer surface area to inner surface area.

Q.

Find the curved surface area of a cone whose radius is 14cm and slant height is 10 cm

1. 440 sq. cm

2. 220 sq. cm

3. 110 sq. cm

4. 240 sq. cm

Q.

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that ${1cm}^3$ of iron has approximately 8 g mass. (Use $\pi =3.14$) [3 MARKS]

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

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

Q. A factory is designed as shown in the figure. There are 150 people working in the factory and each occupy a space of 0.5 $m^3$. The maximum volume available to place machinery in the factory is .

(Take $\pi =\frac{22}{7}$)

1. 5805 $m^3$
2. 8885 $m^3$
3. 5880 $m^3$

Q. Metallic spheres of radii $6cm,8cm$ and $10cm$ respectively, are melted to form a single solid sphere. Find the radius (in cm) of the resulting sphere.

Q. A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm $\times$ 3 cm $\times$ 4 cm. Find the volume of wood in the solid object.

1. $3918c{m}^3$
2. $7024c{m}^3$
3. $1444c{m}^3$
4. $789c{m}^3$

Q.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

1. 0.375

2. 0.125

3. 0.875

4. 0.625

Q.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

1. 0.375

2. 0.625

3. 0.125

4. 0.875

Q. Pair the given solids with their corresponding formula to find the volume.

1. Sphere
2. Cube
3. Cylinder
4. Cuboid
5. Cone
6. $l^3$
7. $\pi r^{2}h$
8. $lbh$
9. $\frac{1}{3}{\mathrm{\pi r}}^{2}h$
10. $\frac{4}{3}{\mathrm{\pi r}}^3$

Q.

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c{m}^2$).

1. $56c{m}^2$

2. $40c{m}^2$

3. $52c{m}^2$

4. $48c{m}^2$