Curved Surface Area of a Right Circular Cylinder

Q.

Question 6

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹ 15 $(Take\pi =3.14)$

Q.

A cylinder of circumference 8 cm and length 21 cm rolls without sliding for $4\frac{1}{2}$ seconds at the rate of 9 complete rounds per second.

Find:

(i) the distance travelled by the cylinder in $4\frac{1}{2}$ seconds, and

(ii) the area covered by the cylinder in $4\frac{1}{2}$ seconds.

Q.

In Fig. there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate the cost of painting the shaded region at the rate of ₹25 per $c{m}^2$.

1. ₹10

2. ₹309

3. ₹253

4. ₹800

Q.

The cost of painting curved surface area of a cylindrical pillar of height $10m$ and radius $3.5m$ at $\text{Rs.}10$ per sq. meter is $\text{Rs.}2200.$
$(\text{Take}\pi =\frac{22}{7})$

1. True

2. False

Q.

The length, breadth and height of a rectangular solid are in the ratio 6 : 5 : 4. If the total surface area is 5328 $c{m}^2$ , find the length, breadth and height of the solid.

Q.

Prove that the surface area of a solid hemisphere is equal to the curved surface area of circumscribed cylinder.

Q.

Find the surface area (in cm sq.) of a container with radius 4 cm and height 10 cm, The container is open from the top.

1. 301.6
2. 351.9
3. 251.3
4. 421.6

Q.

The cost of painting curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹10 per $m^2$ is ₹ 2200.
(Take $\pi =\frac{22}{7}$)

1. True

2. False

Q.

A metal pipe is 77 cm long. The inner diameter of a cross-section is 4 cm, the outer diameter being 4.4 cm. Select the statements that hold true.

$[Assume\pi =\frac{22}{7}]$

1. Inner curved surface area $=968c{m}^2$

2. Outer curved surface area $=1064.8c{m}^2$

3. Total surface area $=2038.08c{m}^2$

4. Total surface area $=6758.08c{m}^2$

Q.

A big iron boiler tank has a cylindrical structure which is open from the top. Its height is 10 m and radius is 7 m. It gets painted at a rate of 3 m${}^2$ per day. Then find the number of days in which the tank gets painted completely? (Take $\pi =\frac{22}{7}$)

1. 192

2. 198

3. 208

4. 202

Q.

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

$[Assume\pi =\frac{22}{7}]$

1. $410m^2$

2. $210m^2$

3. $190m^2$

4. $110m^2$

Q.

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior.The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm.If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
$[Assume\pi =\frac{22}{7}]$

1. Volume of wood = $=3.28c{m}^3$

   Volume of the graphite$=0.11c{m}^3$

2. Volume of wood = $=5.28c{m}^3$

   Volume of the graphite$=0.19c{m}^3$

3. Volume of wood = $=5.28c{m}^3$

   Volume of the graphite$=0.11c{m}^3$

4. Volume of wood = $=9.28c{m}^3$

   Volume of the graphite$=0.41c{m}^3$

Q.

A road roller used for levelling a road of width 2m. It was observed that, the road roller required 25 complete revolutions to complete the levelling of road. If the diameter and length of roller is 7m and 2m respectively, then length of road is [use $\pi$ = 3.14].

1. 1100 m

2. 1234 m

3. 1099 m

4. 1999 m

Q. 56. A right circular cylinder just encloses a sphere of radius r. Find: (1) surface area of the sphere, (2) curved surface area of the cylinder, (3) ratio of the areas obtained in (1) & (2).

Q. It costs Rs.$2200$ to paint the inner curved surface of a cylindrical vessel $10m$ deep. If the cost of painting is at the rate of Rs.$20$ per $m^2$. Find capacity of the vessel.

1. $96.25$ $m^3$
2. $56.25$ $m^3$
3. $96.75$ $m^3$
4. $91.25$ $m^3$

Q. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

Q.

The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹ 10 per sq. meter is:
(Take pi=$\frac{22}{7}$)

1. ₹ 2200

2. ₹ 1100

3. ₹ 550

4. ₹ 4400

Q.

A right circular cylinder just encloses a sphere of radius r (see figure). Find the curved surface area of the cylinder.

1. $3\pi r^2$

2. $12\pi r^2$

3. $9\pi r^2$

4. $4\pi r^2$

Q. If a rectangular sheet is folded along its length to cover the curved surface of the cylinder with radius R and height H, then find the length and breadth of the rectangular sheet.
$\left[2Marks\right]$

Q.

A cylindrical container of depth 20 m and radius 0.7 m is painted for Rs.8800. If the painter takes Rs.40 per sq. meter to paint the cylindrical container, then find the CSA of the cylindrical vessel.

1. 192.5

2. 385

3. 96.25

4. 770

Q.

The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is:

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

Q.

In a circus, a motorcyclist performs his stunts in a death-well which is in the form of a hollow cylinder. The thickness of the cylinder is negligible. If the diameter of the hollow cylinder is 14 m, and height is 20 m, then find the area available for the motorcyclist to perform stunts. (Take $\pi =\frac{22}{7}$)

1. 616m²

2. 516m²

3. 486m²

4. 586m²

Q. The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is $1056$ $c{m}^2$ and the volume of material in it is $1056$ $c{m}^3.$Find the sum of its internal and external radii. Given that the height of the cylinder is $21cm$.

Q.

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of ₹ 12.50 per $m^2.[Assume\pi =\frac{22}{7}]$

1. ₹ 78.75

2. ₹ 68.75

3. ₹ 98.75

4. ₹ 48.75

Q. Rukhsar painted the outside of the cabinet of measure $1$ m, $2$ m, $1.5$ m. How much surface area did she cover, if she painted all except the bottom of the cabinet.

Q. It costs Rs.$2200$ to paint the inner curved surface of a cylindrical vessel $10m$ deep. If the cost of painting is at the rate of Rs.$20$ per $m^2$. Find radius of the base.

1. $1.25m$
2. $3.75m$
3. $2.75m$
4. $1.75m$

Q. State True(1) or False(0).

Q. Answer the following question from the given figure.
Here the solid is composed of cube, cylinder and cone.
Here,
The curved surface area of cone is P.
The curved surface area of cylinder is Q.
The area of the base of cone and cylinder is R and the Total surface area of cube is S.
Then, find the total surface area of solid.

1. P + Q - 2R + S
2. P + Q + 2R + S
3. P + Q + R + S
4. P + Q - R + S

Q. A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3:4

Q.

The diameter of a roller 84 cm long is 1.5 m. If it takes 100 revolutions to level a playground, find the cost of levelling this ground at the rate of ₹ 0.50 per square metre.

1. ₹ 99

2. ₹ 396

3. ₹ 108

4. ₹ 198