Volume of a solid

Q.

A well of diameter 3m is dug 14m deep. The earth taken out of it has been evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

1. 2.0 m

2. 2.95 m

3. 3.87 m

4. 1.125 m

Q. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is V find the total area around the fountain that gets wet.

Q. A solid is in the form of a right circular cylinder, with a hemisphere at one end and a cone at the other end. The radius of the common base is 3.5 cm and the heights of the cylindrical and conical portions are 10 cm. and 6 cm, respectively. Find the total surface area of the solid. (Use π = 22/7)

Q. Find the length of longest rod that can fit in a cuboid of dimensions 6cm × 3cm × 2cm .

Q. The surface area of a sphere is the same as the curved surface area of a cone having the radius of the base as 120 cm and height 160 cm. Find the radius of the sphere.

Q.

What is a hub in a centriole?

Q.

Find the area of the canvas required to make a conical tent 14m high and 96m in diameter. Given that:
1) canvas used in folds and stitchings is 20% of the curved surface area of the tent.

Q.

How many gold coins of 1.75cm in diameter and 2mm in thickness can be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5cm?

1. 550

2. 350

3. 500

4. 400

Q. The given figure represents a hemisphere surmounted by a conical block of wood. The diameter of their bases is 6 cm each and the slant height of the cone is 5 cm. Calculate:
(i) the height of the cone.
(ii) the volume of the solid. [4 MARKS]

Q.

A soft drink is available in two packs - (i) a tin can with a rectangular base of length $5cm$ and width $4cm$, having a height of $15cm$ and (ii) a plastic cylinder with circular base of diameter $7cm$ and height $10cm$. Which container has greater capacity and by how much?

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

Q. Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.

Q.

A well of whose diameter is 3m is dug 14m deep. The earth taken out of it is evenly spread out in the form of a circular ring of width 4m to form an embankment. Find the height of the embankment.

1. 3.87 m

2. 2.95 m

3. 2.0 m

4. 1.125 m

Q.

What is the diagonal length of a TV screen whose dimensions are 80 x 60 cm?

1. 1000

2. 10

3. 100

4. 200

Q.

The ratio of the base-radii of two cones is 3 : 5 and their heights are in the ratio 2 : 3. What is the ratio of their volumes?

Q. A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is

(a) 1 : 3

(b) 1 : $\sqrt{3}$

(c) 1 : 1

(d) $\sqrt{3}$ : 1

Q. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape formed.

Q. Question 5
Two identical cubes each of volume $64c{m}^3$ are joined together end to end. What is the surface area of the resulting cuboid?

Q. Find the total surface area of a cube whose volume is $64m^3.$

1. $24m^2$
2. $4m^2$
3. $96m^2$
4. $64m^2$

Q. The length of a medicine capsule is 14mm and the diameter is 5mm. Find its surface area in $m{m}^2$.

1. 220

Q. A cylindrical container whose diameter is 12 cm and height is 15 cm is filled with ice cream. The whole ice cream is distributed to 10 children in equal cones having a hemispherical top. If the height of the conical portion is twice the diameter of its base then find the diameter of the ice cream cone.

Q.

There is a coin. Ram attaches a conical attachment to one flat end of coin. The conical attachment has same radius as coin. What is the surface area of the combined solid?

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 coin + total surface area of cone

4. Total surface area of cone

Q. A tent is in the form of a cylinder of diameter 20 m and height 2.5 m, surmounted by a cone of equal base and height 7.5 m. Find the capacity of the tent and the cost of the canvas at Rs 100 per square metre.

Q.

The height of a conical tent is 28 m and the diameter of the base is 42 m. Find the cost of the canvas used at Rs 20/- per sq. m.

Q. A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m. [CBSE 2012]

Q.

If the object is solid, the space occupied by such an object is called volume and if the object is hallowed, the space that can be filled is called____

Q.

a circus tent is cylindrical in shape up to a height of 4.2 m and conical above it. the common diameter of the base of the cylindrical and conical parts is 6 m. if the total height of the tent from the ground is 8.2 m, find the cost of canvas needed to make the tent at the rate of Rs.160 per m²

Q. Howany silver coins, 1.75 cm in diameter and of thickness 2mm, must be melted to form a cuboid of dimensions 5.5cm x 10cm x 3.5 cm?
(only calculation part)

Q.
Find the inner surface area of the above vessel.

1. 572

Q.

A field is 80 m long and 50 m broad. In one corner of the field a pit which is 10 m long, 7.5 m broad and 8 m deep has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. If the rise in the level of the field is x(in cm), then x-0.3 =

___

Q. Question 2
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.