Surface Area of a Cylinder

Q. Question 6
The radii of two cylinders are in the ratio of 2:3 and their heightsare in the ratio of 5:3. The ratio of their volumes is:

A) 10:17
B) 20:27
C) 17:27
D) 20:37

Q. The diameter of the base of a right circular cylinder is 20 m and its height is 42 m. Find its curved surface area.

1. 2210 $m^2$
2. 1320 $m^2$
3. 5386 $m^2$
4. 5280 $m^2$

Q.

The circumference of the base of cylindrical vessel is $132cm$ and its height is $25cm$. How many litres of water can it hold? $\left(1000c{m}^3=1L\right)$ (Assume $\mathrm{\pi }=\frac{22}{7}$)

Q.

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $Rs20per{m}^2$, find the radius of the vessel.

1. $1.75m$

2. $4.75m$

3. $3m$

4. $3.5m$

Q.

It costs $Rs2200$ to paint the inner curved surface of a cylindrical vessel $10m$ deep. If the cost of painting is at the rate of $Rs20$per $m^2$, find

(i) inner curved surface area of the vessel

(ii) radius of the base

(iii) capacity of the vessel (Assume $\pi =\frac{22}{7}$)

Q. The radius of the base of a right circular cone is 21 cm and its height is 20 cm. Find the curved surface area of the cone.

1. $1914c{m}^2$
2. $1386c{m}^2$
3. $3300c{m}^2$
4. $26720c{m}^2$

Q.

The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm.

How many litres of water can it hold? $(1000c{m}^3=1l)$

1. 69.3
2. 85.6
3. 34.65
4. 22.4

Q.

A cylindrical roller of radius 8 m and height 20 m is to be painted. The ends are to be painted in red and the curved surface is to be painted in blue. If the cost of painting in red is $₹2.1per{m}^2$ and the in blue is $₹1.4per{m}^2$, what is the total cost of painting?

1. 20

2. 16

3. 18

4. 12

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

Q. A Rectangular paper of width $14$ cm is rolled along its width and a cylinder of radius $20$ cm is formed. Find the volume of the cylinder?

1. $18560$ cu. cm
2. $17500$ cu. cm
3. $17600$ cu. cm
4. $18000$ cu. cm

Q. If the diameter of a cylinder is $28cm$ and it height is $20cm$, then its curved surface area is

1. $1760{cm}^2$
2. $820{cm}^2$
3. $2460{cm}^2$
4. $3520{cm}^2$

Q. The volume of a cube with lateral surface area 100 cm² is ______ .

1. 125 cm³
2. 120 ${\text{cm}}^3$
3. 100 ${\text{cm}}^3$
4. 150 ${\text{cm}}^3$

Q. The curved surface area of the cylinder is $1760c{m}^2$ and its volume is $12320c{m}^3.$ Find its height.

Q. If the radii of two cylinders are in the ratio 2:3 and their heights are in the ratio of 5:3, then what is the the ratio of their volumes?

1. 27:17
2. 20:24
3. 20:27
4. 24:30

Q. A rectangular paper of width $14$ cm is rolled along its width and a cylinder of radius $20$ cm is formed. What will be volume of the cylinder ?

1. $17600$ $c{m}^3$
2. $16600$ $c{m}^3$
3. $156600$ $m^3$
4. None of these

Q.

The total surface area of a right circular cylinder of height 9m is 440 sq. meter.Find the radius of the cylinder. (Take~$\pi =\frac{22}{7}$)

Q.

If cloth costs $₹10/m^2$ then find the total cost to build a cloth pyramid of base edge 10 m and slant height 10 m.

1. ₹ 3000

2. ₹ 1000

3. ₹ 2000

4. ₹ 4000

Q. The lateral surface area of cylinder is $176{cm}^2$ and base area 38.5${cm}^2$. The volume is ..............

1. $830{cm}^3$
2. $380{cm}^3$
3. $308{cm}^3$
4. $803{cm}^3$

Q. A solid cylinder has total surface area of 1386 $c{m}^2$. Its curved surface area one-ninth of its total surface area. Find the radius and height of the cylinder.

Q.

The total surface area of a right circular cylinder of height 9m is 440 sq. meter.Find the radius of the cylinder. (Take π = 22/7)

Q. If curved surface area and circumference at the base of a solid right circular cylinder are $4400sq.cm$ and $110cm$ respectively. Find its height .

Q. The number of surface areas in right circular cylinder is

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

Q. A formula for the surface area $\left(A\right)$ of the rectangular solid shown below is $A=2lw+2lh+2wh$ where $l$ represents length; $w$, width; and $h$, height. By doubling each of the dimensions ($l,w$, and $h$), the surface area will be multiplied by what factor?

1. $2$
2. $8$
3. $6$
4. $4$

Q. The radius of base and the height of a right circular cylinder are each increased by 20%. The volume of the cylinder will increase by

1. 72.8%
2. 60%
3. 40%
4. 96%

Q.

Question 6
The radii of two cylinders are in the ratio of 2:3 and their heightsare in the ratio of 5:3. The ratio of their volumes is:

A) 10:17
B) 20:27
C) 17:27
D) 20:37

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

Q.

The total surface area of a right circular cylinder of height 9m is 440 sq. meter.Find the radius of the cylinder. (Take π = 22/7)

1. 2.5m

2. 5m

3. 7.5 m

4. 10m

Q. A well is $7.2m$ deep. The cost of cementing its inner surface at $75$ paise per $d{m}^2$ is Rs. $11880$. Determine the radius of the wall.

Q. An open box is constructed by starting with a rectangular sheet of metal 10 cm by 14 cm, and cutting a square of side x cm from each corner. The resulting projections are folded up and the seams welded. The volume of the resulting box is:

1. $140x+48x^2+4x^3$
2. $140x-24x^2+x^3$
3. none of these
4. $140x+24x^2+x^3$
5. $140x-48x^2+4x^3$

Q. John's birthday cake is a delightful cylinder of radius 6 inches and height 3 inches. If these friends cut the cake into 8 equal sectors, then the total surface area of a piece of birthday cake in sq. inches is

1. $9(\pi +4)$
2. $\frac{27\pi }{2}$
3. $4(\pi +4)$
4. $\frac{9}{2}(3\pi +8)$