Volume of combined figures

Q.

A right triangle ABC with sides $5cm$, $12cm$ and $13cm$ is revolved about the side $12cm$. Find the volume of the solid so obtained.

Q.

Volume of a cuboidal pencil box is V. It consists of 10 pencils each of volume v . Find the remaining volume.

1. V-v

2. v-V

3. V-10v

4. 10v-V

Q.

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

$2p,4q,8r$

Q.

A toy in shape of a sphere of radius 7cm is surmounted by a cone of height 11cm. Find the volume of the toy.

1. 2001cm³

2. 2000cm³

3. 1001cm³

4. 1000cm³

Q.

A tank having a capacity of $4096m^3$ is used by 4 families. If each family uses 4 buckets of water every day and the volume of the bucket is $16m^3$, then the water in the tank will last for at least how many weeks?

1. 2

2. 3

3. 1

4. 4

Q.

A building is in the form of a cuboid with an overhead tank in the form of a cylinder such that the tank spans halfway across the length of the building. Find the volume of the entire structure if the dimensions of the building is $20m\times 10m\times 20m$ and the height of the tank is 5m.

1. 4000 + 500π

2. 4000 + 125π

3. 4400 + 250π

4. 4000 + 250π

Q.

Find the volume of the figure.

1. 7141.2

2. 3181.2

3. 5162.5

4. 7142.8

Q.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

1. 523.53 $c{m}^3$

2. 550 $c{m}^3$

3. 576.63 $c{m}^3$

4. 456.89 $c{m}^3$

Q.

Volume enclosed between a cylindrical vessel consisting of 2 concentric cylinders is 90$\pi$ $m^3$. If outer radius is 5m and height of the cylinder is 10m. Find the thickness of the cylindrical vessel.

1. 1m

2. 1.5m

3. 2m

4. 2.5m

Q.

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

1. 20000

2. 20500

3. 18500

4. 19500

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.

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 =

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

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

Q. If two cubes of volume $216m^3$ are joined end to end to form a cuboid, then find the volume and total surface area of the cuboid.

1. $432m^3,380m^2$
2. $216m^3,160m^2$
3. $432m^3,360m^2$
4. $430m^3,180m^2$

Q.

Find the volume of the given shape.

1. 20000mm³

2. 24000mm³

3. 48000mm³

4. 10000mm³

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

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

Q.

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

1. 110

2. 100

3. 210

4. 200