Answer:
Step-by-step explanation:
Given: Cylinder
Curved Surface = 2(Area of Base)
Sum radius and height = 28 cm.
Find: Volume of Cylinder
Plan: Let’s look at the various formulas involved.
For example:
Volume of Cylinder(V) = Base Area x Height The Base is a Circle. Therefore: V = πr^2h
Curved Surface Area is called the Lateral Area(LA) Now: LA = Circumference x Height. Therefore: LA = 2πrh. From the Given, it is also 2(Area of Base) => LA = 2(πr^2)
(r + h) = 28 cm.
From statement 2, we have 2 formulas for LA. Thus,
2πrh = 2πr^2 => dividing both sides of the equation by 2πr => h = r ✅
From statement 3, therefore r = h = 7 cm. each
Now we are ready. Using statement 1, and substituting:
V = πr^2h => V = π(7)^2(7) = π(343) = 343π cm^3 ✅
Double Check: Reasonable/Re verified/Recalculated ✅ ✅
Answer: Volume of Cylinder = 343π cm^3 or 1,077.57 cm^3 approximately using π ≈ 3.1416