Advertisements
Advertisements
Question
A glass cylinder with a diameter 20 cm water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder. (Take π = 3.142)
Solution
Suppose the water rises by h cm.
Clearly water in the cylinder forms a cylinder of height h cm and radius 10 cm.
∴ The volume of the water displaced = Volume of the cube of edge 8 cm.
⇒ πr2h = 83
⇒ 3.142 x 102 x h = 8 x 8 x 8
⇒ `(8 xx 8 xx 8)/(3.142 xx 10 xx 10)` cm = h
⇒ h = 1.6 cm.
APPEARS IN
RELATED QUESTIONS
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find (i) radius of its base (ii) its volume. [Use π = 3.14]
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 Rs 20 per m2, find
(i) Inner curved surface area of the vessel
(ii) Radius of the base
(iii) Capacity of the vessel
`["Assume "pi=22/7]`
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small container each of diameter 3 cm and height 4 cm. How many container are necessary to empty the bowl?
From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed. Find the volume of the remaining solid.
A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π = 3.14]
A cylindrical container with diameter of base 42 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 22 cm × 14 cm × 10.5 cm. Find the rise in the level of the water when the solid is submerged.
Water is being pumped out through a circular pipe whose external diameter is 7 cm. If the flow of water is 72 cm per second how many litres of water are being pumped out in one hour.
Water flows through a cylindrical pipe of internal diameter 7 cm at 36 km/hr. Calculate the time in minutes it would take to fill the cylindrical tank, the radius of whose base is 35 cm, and height is 1 m.
Find the number of coins, 1.5 cm in diameter and 2 mm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm
A rectangular sheet of paper is rolled in two different ways to form two different cylinders. Find the volume of cylinders in each case if the sheet measures 44 cm × 33 cm.
