2. Brian is filling a conic container with water. He has the container half full. The radius of the container is 5 inches and the height is 20 inches. (a) What is the current volume of the water? Show your work and explain your steps. (b) If Brian wants to transfer the water to a cylinder with a radius of 5 inches, and fill it completely, what height would the cylinder have to be? Show your work and explain your steps.

current volume of the water = 785.714 in²

Height of new container = 10 inches

Step-by-step explanation:

Radius of the container = 5 inches

Height of the container = 20 inches

Volume of the container = πR²H = (22/7) × 5² × 20 = 1571.428571428 in²

Since the container is half filled with water, volume of the water = 1571.428571428 ÷ 2 = 785.714 in²

b. Volume of cylinder = πR²H = volume of water from first container = 785.714 in²

Hence 785.714 = (22/7) × 5² × H

H = (785.714) ÷ [(22/7) × 25] = 10 inches

Height of new container = 10 inches

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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