Find r if T.A=12Pi and L.A =8Pi
sounds like a cylinder.
2πr^2 + 2πrh = 12π
2πrh = 8π, so
2πr^2 + 8π = 12π
2πr^2 = 4π
r^2 = 2
r = √2
and r = √6
To find r, we need to know the formulas for the total area (T.A) and lateral area (L.A) of a solid. Since you mentioned Pi, we'll assume you're referring to a cylinder.
The formulas for the total area and lateral area of a cylinder are:
T.A = 2πr² + 2πrh
L.A = 2πrh
Given:
T.A = 12π
L.A = 8π
We have two equations with two unknowns (r and h). To solve for r, we can substitute the value of L.A into the L.A formula and solve for h:
8π = 2πrh
Dividing both sides by 2π, we get:
4 = rh
Now, substitute the value of h from this equation into the T.A formula:
12π = 2πr² + 2π(4)
Simplifying, we have:
12π = 2πr² + 8π
Subtracting 8π from both sides:
4π = 2πr²
Dividing both sides by 2π:
2 = r²
Taking the square root of both sides, we find:
r = √2
So, the value of r is the square root of 2.