What is the maximum possible volume of a cylinder?

Therefore the volume is a maximum when 2r−2h+h=0, so h=2r and hr=2. Let the ratio of height to radius be ρ, then h=ρr. The volume of the cylinder is V=πr2h=πρr3. Let k=h/r, where h is the height and r is the radius.

How do you write the volume of a cylinder in terms of pi?

The formula that is used to determine the volume of the cylinder in terms of pi is V = πr2h cubic units where, “V”, “r” and “h” are the volume, radius, and height of the cylinder. This formula of volume of the cylinder also shows its dependence on the radius and height of the cylinder.

What if the formula for the volume of a cylinder?

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . Simplify.

Why does the formula for the volume of a cylinder include πr2?

Thus, the volume of the cylinder can be given by the product of the area of base and height. For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height. Therefore, the volume of a cylinder = πr2h cubic units.

How do you answer in terms of pi?

Question: Can you work out the perimeter of a semicircle with a radius of 3cm? Give your answer in terms of pi? Answer: To work out the cirumference multiply the diameter by pi. The diameter is 6, and so 6 multiplied by Pi is 6Pi.

What is the meaning of maximum volume?

1 the greatest possible amount, degree, etc. 2 the highest value of a variable quantity.

How do you find the volume of a cylinder using Formula?

So using the volume of cylinder formula we can find the volume of it. V = π· r 2· h. V = π· 7 2· 11. V = 1692.46 m 3 = 1692.46 kl . Example 2: Find the volume of a cylinder whose base radius is 6 cm and height is 4 cm.

What is the circumference of the base of a liquid cylinder?

The volume of the liquid is the same no matter it is in the vessel or in the cylinder, therefore we have: V1 = V2, where V1 is the volume of the vessel and V2 is the volume determined using the formula for a cylinder. Thus: And the circumference of its base is 66 cm.

What is the volume of a hollow cylinder in cubic units?

Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder Therefore, the volume of a cylinder = πr2h cubic units. In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed by the base of hollow cylinder.

What is the surface area of a cylinder?

A cylinder has a radius (r) and a height (h) (see picture below). This shape is similar to a soda can. The surface area is the area of the top and bottom circles (which are the same), and the area of the rectangle (label that wraps around the can)