Question
πr2×r=2
Solve the equation
r=π32π2
Alternative Form
r≈0.860254
Evaluate
πr2×r=2
Multiply
More Steps

Evaluate
πr2×r
Multiply the terms with the same base by adding their exponents
πr2+1
Add the numbers
πr3
πr3=2
Divide both sides
ππr3=π2
Divide the numbers
r3=π2
Take the 3-th root on both sides of the equation
3r3=3π2
Calculate
r=3π2
Solution
More Steps

Evaluate
3π2
To take a root of a fraction,take the root of the numerator and denominator separately
3π32
Multiply by the Conjugate
3π×3π232×3π2
The product of roots with the same index is equal to the root of the product
3π×3π232π2
Multiply the numbers
More Steps

Evaluate
3π×3π2
The product of roots with the same index is equal to the root of the product
3π×π2
Calculate the product
3π3
Reduce the index of the radical and exponent with 3
π
π32π2
r=π32π2
Alternative Form
r≈0.860254
Show Solution

Rewrite the equation
π2x6+3π2x4y2+3π2x2y4+π2y6=4
Evaluate
πr2×r=2
Evaluate
π(x2+y2)r=2
Square both sides of the equation
(π(x2+y2)r)2=22
Evaluate
(π(x2+y2))2r2=22
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
(π(x2+y2))2(x2+y2)=22
Use substitution
(π2x4+2π2x2y2+π2y4)(x2+y2)=22
Evaluate the power
(π2x4+2π2x2y2+π2y4)(x2+y2)=4
Solution
π2x6+3π2x4y2+3π2x2y4+π2y6=4
Show Solution
