Curved surface area of a Right Circular cone

Q. Question 7
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 so formed.

Q.

Diameter of the base of a cone is $10.5cm$ and its slant height is $10cm$. Find its curved surface area.

Q. Question 2
Write ‘True’ or ‘False’ and justify your answer in the following :
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is $4\pi rh+4\pi r^2$.

Q. A child reshapes a cone made up of China clay of height $24cm$ and radius of base $6cm$ into a sphere. The radius of the sphere is:

1. $24cm$
2. $12cm$
3. $6cm$
4. $48cm$

Q. From a solid cylinder whose height is $2.4$ cm and diameter $1.4$ cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c{m}^2$. (Use $\pi =\frac{22}{7}$).

Q. The radius and slant height of a cone are in the ratio $4:7$. If its curved surface area is $792c{m}^2$, find its radius $(\pi =22/7)$.

Q. A sector containing an angle of ${120}^{\circ }$ is cut off from a circle of radius $21$ cm and folded into a cone by joining the radii. Find the curved surface area of the cone. $(\pi =\frac{22}{7})$

Q.

How many metres of cloth $5m$ wide will be required to make a conical tent, the radius of whose base is $7m$ and whose height is $24m$?

Q. Curved surface area of a cone is $308c{m}^2$ and its slant height is $14$cm. Find the radius of the base and total surface area of the cone.

Q. A tent is cylindrical to a height of $4.8$ m and conical above it. The radius of the base is $4.5m$ and the total height of the tent is $10.8$. Find the approximate area of the canvas required for the tent in square meters.

Q. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent

1. 9735
2. 9730
3. 9720
4. 9710

Q. From a circle of radius $15$ cm, a sector with ${216}^o$ angle is cut out and its bounding radii are bent so as to form a cone. Then its volume is:

1. $1081.3{cm}^3$
2. $1071{cm}^3$
3. None of these
4. $1018{cm}^3$

Q. The slant height and base diameter of a conical tomb are $25m$ and $14m$ respectively. Find the cost of white-washing its curved surface at the rate of $Rs.210$ per $100m^2$.

Q. The radius of the base and the height of a right circular cone are $7$ cm and $24$ cm respectively Find the total surface area of the cone

1. $70.4$ cm${}^2$
2. $704$ cm${}^2$
3. $7.04$ cm${}^2$
4. $0.704$ cm${}^2$

Q. Find the surface area of a cone.

1. $8635m^2$
2. $86.35m^2$
3. $0.8635m$
4. $8.635m^2$

Q.

The curved surface area of a cylinder is 250 sq.cm. If the circumference of its base is 25cm, then its height is ____.

1. 5 cm

2. 50 cm

3. 10 cm

4. 2 cm

Q. A right circular triangles with sides $12$ cm and $16$cm is revolved around its hypotenuse. Find the volume of the double cone so formed.

1. $1930.97c{m}^3$
2. $1234.97c{m}^3$
3. $1710.95c{m}^3$
4. $1536.2c{m}^3$

Q. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm , a concial cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm.

Q. Radius and slant height of a solid right circular cone are in the ratio $3:5$. If the curved surface area is $60\pi sq.cm$, then find its total surface area.

1. $301\frac{5}{7}{cm}^2$
2. $31\frac{5}{7}{cm}^2$
3. None of these
4. $302\frac{5}{7}{cm}^2$

Q. The area of canvas required to construct a cone of height 24 m and base radius 7 m is

1. $500m^2$
2. $520m^2$
3. $550m^2$
4. none of these

Q. In the given figure $PQRS$ is a cyclic quadrilateral $PQ$ and $SR$ produced meet at $T$. Find area of quadrilateral $PQRS$ if area of $△PTS=27c{m}^2$ (given Triangle TPS is similar to TRQ)

Q. $AB$ is chord parallel to $MNS$. If $AB=4$cm, then $AC=$

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

Q. The longest needle that can be placed in a cylinder of radius r units and height h units is _____ (in units)

1. $\sqrt{4r^2+h^2}$
2. $\sqrt{3r^2+h^2}$
3. $\sqrt{4r^2-h^2}$
4. $\sqrt{3r^2+2h^2}$

Q. A sphere of radius $r$ is inscribed in the cylinder such that the curved surface of the sphere touches the cylinder as shown in the given figure. The area of curved surface of cylinder is

1. $\frac{4}{3}\pi r^2$
2. $4\pi r^2$
3. $\pi r^2$
4. $2\pi r^2$