Curved Surface Area of a Right Circular Cone

Q.

The curved surface area of a cylinder of height 14 cm is 88 sq. cm. The diameter of the cylinder is 1cm.

1. 1.5

2. 2

Q.

A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [Approximately]

1. 100 grains

2. 531 grains

3. 230 grains

4. 700 grains

Q. The volume of a conical tent is 1232 $m^3$ and the area of the base floor is 154 $m^2$. Calculate the:
i) radius of the floor;
ii) height of the tent;
iii) length of the canvas required to cover this conical tent if its width is 2 m [4 MARKS]

Q.

Find the volume and surface area of a cone with diameter 8 cm and height 8 cm.

Q.

There is a tent in a conical shape. The slant height of the tent is 14 m. If the curved surface area of the tent is 308 m² , then what is the base area of the tent? (Take $\pi =\frac{22}{7}$)

1. 132

2. 224

3. 254

4. 154

Q. If a cone has a radius of 5 cm and height of 12 cm, then match the following.

1. 13 cm
2. $90\pi c{m}^2$
3. $65\pi c{m}^2$

Q. The curved surface area of a cone of radius 'r', height 'h' and slant height 'l' is ___.

1. $\pi rl$
2. $r+l$
3. $\pi rl(l+h)$
4. $2\pi l$

Q.

If the radii of the circular ends of a bucket 24 cm high are 5 cm and 15 cm respectively, find the surface area of the bucket.

Q. Question 2 (i)
Find the capacity in litres of a conical vessel with:
(i) radius 7 cm, slant height 25 cm.
$[Assume\pi =\frac{22}{7}]$

Q. Question 2
A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed.

Q.

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

1. 12 cm

2. 15 cm

3. 16 cm

4. 18 cm

Q. If two cones have equal diameters and their slant heights are in the ratio 3 : 4, then ratio of their CSA is .

1. 3 : 5
2. 3 : 4
3. 5 : 3

Q. The CSA of a cylindrical container of depth 20 m and radius 0.7 m =.

1. 22 m${}^2$
2. 44 m${}^2$
3. 88 m${}^2$

Q. 27. If the perimeter of a semicircular protactor is 36cm, find its diameter

Q.

The curved surface area of a cone of slant height $l$ and radius $r$ is given by

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

2. $\pi rl$

3. $\pi r{l}^2$

4. $\frac{1}{3}\pi rl$

Q.

A cone of radius 3 cm and slant height 5 cm has a curved surface area of ___ $c{m}^2$.

1. 16π

2. 13π

3. 14π

4. 15π

Q.

A conical tomb is made up of bricks whose surface area is 5 m${}^2$. The slant height and radius of the tomb are measured to be 25 m and 7 m respectively. The approximate number of bricks used to construct the tomb are ____ (Take $\pi =\frac{22}{7}$)

1. 100

2. 110

3. 150

4. 160

Q. A corn cob shaped somewhat like a cone, has the radius of its broadest end as 2.1 cm and length as 20 cm. If each 1 sq cm of the surface of the cob carries an average of four grains, find how many grains you would find on the entire cob? [4 MARKS]

Q.

A right-angled triangle having its height and base equal to 24 cm and 7 cm respectively is rotated by 360⁰ along its base. Find the curved surface area of the resultant figure.

1. 520 cm²

2. 450 cm²

3. 1460 cm²

4. 550 cm²

Q.

In a farm, a heap of paddy is in the form of a cone with slant height 13 m and height 12 m. What is the area of canvas needed to protect it from sun and rain?

Q. A heap of wheat is in the form of a cone whose diameter is $10.5m$ and height is $3m$. Find its volume.
The heap is to be covered by canvas to protect it from the rain. Find the area of the canvas required (in $m^2$).
$[Assume\pi =\frac{22}{7}]$

1. 99.825

Q.

If the area of a circle with radius $r$ is equal to the curved surface area of cone with radius $r_1$ and slant height $l$ then the value of $r_1$ in terms of $r$ and $l$ is:

1. None of these

2. =

3. = rl

4. = rl

Q.

The height of a cone is 8 cm and its base radius is 6 cm. The curved surface area the cone is (Use $\pi$ = 3.14).

Q. The height of a conical tent is $14m$ and its floor area is $346.5m^2$. The length of canvas, $1.1m$ wide, required for it is:

1. $490m$
2. $525m$
3. $665m$
4. $860m$

Q.

If the radii of the ends of a bucket 45 cm high are 28 cm and 7 cm respectively, the total surface area of the bucket is:

1. 7074 cm²

2. 8074 cm²

3. 8274 cm²

4. 6074 cm²

Q.

If the area of a rectangle is equal to the curved surface area of the cone, then find the breadth of the rectangle in terms of radius$\left(r\right)$, slant height$\left(h\right)$ and length $\left(l\right)$.

1. $\frac{\pi lh}{r}$
2. $\frac{\pi rl}{h}$

3. $\frac{hrl}{\pi }$

4. $\frac{\pi rh}{l}$

Q. The radii of two right circular cylinders are in the ratio 3 : 4 and their heights are in the ratio 1 : 2. Calculate the ratio of their curved surface areas

Q.

A conical tomb is made up of bricks of a front surface area of $5$ sq. m. The slant height and radius of the tomb are measured to be $25m$ and $7m$ respectively. The approximate number of bricks used to construct the tomb are ___ $(\text{Take}\pi =\frac{22}{7})$

1. 160

2. 100

3. 110

4. 150

Q.

A circular ground of radius 50 m has to be covered with water proof sheet. The same amount of water proof sheet is also used for making conical tents. If the base area of tent is 625 $m^2$then the height of tent is____${cm}^2$

1. 90.42

2. 96.8

3. 100.6

4. 88.5

Q.

If the area of a circle of radius r is equal to the curved surface area of a cone with radius $r_1$ and slant height l, then the value of $r_1$ in terms of r and l is:

1. =

2. = rl

3. = rl

4. None of these