A cylindrical tin can, open at the top, of a given capacity has to be constructed, show that the amount of the tin required will be least if the height of the can is equal to its radius.

A cylindrical tin can , closed at both ends of a given volume , has to be constructed . Prove that , the amount of tin required will be least , when the height of the can is equal to its diameter .

An open tank of a given capacity has square base with vertical sides . Prove that the expense of lining the the tank with cement will be minimum if the height of the tank is half the width.

A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is (a) 3/4 (b) 5/6 (c) 4/5 (d) none of these

Prove that, a conical tent of given capacity will required the least amount of canvas, when the height is sqrt2 times the radius of the base.

Prove that , a conical tent of given capacity will require the least amount of canvas , when the height is sqrt(2) times the radius of the base .

A tank with rectangular base and rectangular sides , open at the top is to be constructed so that its depth is 2 m and volume is 8m^(3) . If building of tank costs Rs. 70 per square metre for the base and Rs. 45 per square metre for sides, what is the cost of least expensive tank ?

A cylindrical vessel is filled with a liquid such that the thrust on the bottom of the vessel and that on its side wall become equal. Prove that the height of the liquid column in the cylinder is numerically equal to the radius of the vessel.

A cuboidal tank is filled with diesel. That amount of diesel is poured into 240 tins in such a way that each of the tins volume is 15 lit. If the breadth of the tank is 1.5 m and the height of the tank is 3/5th times of its length, then find the height and length of the tank.

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^(3) . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

A conical cap is filled with ice cream. The ice cream forms a hemi-spherical shape on its open top. The height of the hemispherical part is 7 cm, The radius of the hemispherical part equals the height of the come. Then the volume of ice-cream is____