Cylinder

Q.

Use cylindrical shells to find the volume $V$ of the solid.

A sphere of radius $r$.

Q. A right cylindrical container of radius $6cm$ and height $15cm$ is full of ice-cream, which has to be distributed to $10$ children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, Then the radius of the ice-cream cone is _____.

1. $3cm$
2. $4cm$
3. $5cm$
4. $2cm$

Q.

A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10 $\text{m}$ and radius is 7 $\text{m}$. It gets corroded at a rate of 3 ${\text{m}}^2$/day. The number of days it will take to corrode completely is ____ .
$(use\pi =\frac{22}{7})$

1. 192

2. 202

3. 198

4. 208

Q.

A cylindrical container of radius 6cm and height 15cm is filled with chocolate. The chocolate is to be filled into cones of height 12cm and radius 3cm having a hemispherical shape on the top. Find the number of cones that can be filled with the chocolate?

1. 10

2. 15

3. 25

4. 20

Q. Question 5
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.

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 solid piece of iron in the form of a cuboid of dimensions $49cm\times 33cm\times 24cm$ is moulded to form a solid sphere.

The radius of the sphere is

1. $21cm$

2. $23cm$

3. $25cm$

4. $19cm$

Q. From a solid right circular cylinder of height 2.4 cm and radius 0.7 cm, a right circular cone of same the height and same radius is cut out. Find the total surface area of the remaining solid.

Q. A cylindrical bucket of height 10 cm and radius 5 cm is overturned to form a conical heap of sand of radius 2.5 cm. Find the height of the cone.

1. 120 cm
2. 110 cm
3. 130 cm
4. 140 cm

Q. The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is $5$ cm, find the height of the cone.

1. $10$ cm
2. $15$ cm
3. $18$ cm
4. $24$ cm

Q. The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is 20:___.

1. 27

Q. Show that the right circular cone of least curved surface and given volume has an altitude equal to $\sqrt{2}$ times the radius of the base.

Q. A metallic sphere of radius $4.2$ cm is melted and recast into the shape of a cylinder of radius $6$ cm. Find the height of the cylinder.

Q. A tent is of the shape of a right circular cylinder upto a height of $3$ m and then becomes a right circular cone with a maximum height of $13.5$ m above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs. $2$ per sq m, if the radius of the base is $14$ m.

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.

Q. A cone and a cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is $3$ m, then the slant height of the cone (in m) is

1. $3$
2. $6$
3. $4$
4. $7$

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.

Q. A cylindrical bucket of height 10 cm and radius 5 cm is overturned to form a conical heap of sand of radius 2.5 cm. Find the height of the cone.

1. 140 cm
2. 130 cm
3. 120 cm
4. 110 cm

Q. The radius of a right circular cylinder increases at a constant rate.Its altitute is a linear function of the radius and increases three times as fast as radius.When the radius is $1cm$ the altitute is $6cm$. When the radius is $6cm$, the volume is increasing at the rate of $1cu$ cm/s.When the radius is $36cm$, the volume is increasing at a rate of $n$ $cu$ $cm/s$.The value of n is equal to ...

1. $11$
2. $22$
3. $33$
4. $44$

Q. Find the length of the canvas $2$m in width required to make a conical tent $12$m in diameter and $63$m in slant height?

Q. The curved surface area of a cone is 670 cm${}^2$ and its radius is 15cm Find its slant height and total surface area

1. 13770.4 cm${}^2$
2. 1377.04 cm${}^2$
3. 137.704 cm${}^2$
4. 137704 cm${}^2$