Advertisements
Advertisements
Question
In the adjoining diagram, a tilted right circular cylindrical vessel with base diameter 7 cm contains a liquid. When placed vertically, the height of the liquid in the vessel is the mean of two heights shown in the diagram. Find the area of wet surface, when the cylinder is placed vertically on a horizontal surface. (Use π = `22/7`).
Solution
The cylinder has a base diameter of 7 cm, so the radius r is:
r = `7/2 = 3.5 " cm"`
The heights of the liquid when tilted are h1 = 1 and h2 = 6 cm.
∴ h = `(h_1 + h_2)/2`
`\implies` h = `1/2(1 + 6)`,
`\implies` h = `7/2`
`\implies` h = 3.5 cm
Area of wet surface = πr2 + 2πrh
Area of base = πr2
= `22/7 xx (3.5)^2`
= 38.5 cm2
Lateral surface area = 2πrh
= `2 xx 22/7 xx 3.5 xx 3.5`
= `2 xx 22/7 xx 12.25`
= 77 cm2
Total wet surface area = Area of base + Lateral area
= 38.5 cm2 + 77 cm2
= 115.5 cm2
APPEARS IN
RELATED QUESTIONS
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
`["Assume "pi=22/7]`
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of Rs. 3.50
per 1000 cm2.
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions moving once over to level a playground. What is the area of the playground?
The curved surface area of a cylinder is 1320 cm2 and its base had diameter 21 cm. Find the height and the volume of the cylinder.
The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunck is 3 m. Find the volume of the timber that can be obtained from the trunk.
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is ______.
How many solid right circular cylinders of radius 2 cm and height 3 cm can be made by melting a solid right circular cylinder of diameter 12 cm and height 15 cm?
