Answer:
[tex]V = 1218.0375m^{3}[/tex]
[tex]A = 342.9m^{2}[/tex]
Step-by-step explanation:
Area:
[tex]A =[/tex] π [tex]r^{2}[/tex]
[tex]152.4 =[/tex] π [tex](2x)^{2}[/tex] *Square 2x*
[tex]152.4 =[/tex] π [tex]4x^{2}[/tex] *Divide by π*
[tex]48.510 = 4x^{2}[/tex] *Divide by 4*
[tex]12.128 = x^{2}[/tex] *Square root*
[tex]\sqrt{12.128} = x[/tex] *Solve*
x ≈ 3.482
Now take the same equation but replace 2x with 3x
[tex]A =[/tex] π [tex]r^{2}\\[/tex]
Now replace x with 3.482 and solve for area.
[tex]A = 342.9m^{2\\}[/tex]
Volume:
[tex]V = \frac{4}{3}[/tex] π [tex]r^{3}[/tex] *Insert variables*
[tex]360.9 = \frac{4}{3}[/tex] π [tex](2x)^{3}[/tex] *Cube 2x*
[tex]360.9 = \frac{4}{3}[/tex] π [tex](8x^{3})[/tex] *Multiply [tex]\frac{3}{4}[/tex] on both sides*
[tex]270.675 =[/tex] π [tex](8x^{3})[/tex] *Divide by π*
[tex]86.159 = 8x^{3}[/tex] *Divide by 8*
[tex]10.770 = x^{3}[/tex] *Cube root*
[tex]\sqrt[3]{10.770} = x[/tex] *Solve*
x ≈ 2.208
Now take the same equation but replace 2x with 3x
[tex]V = \frac{4}{3}[/tex] π [tex](3x)^{3}[/tex]
Now replace x with 2.208 and solve for volume.
[tex]V = 1218.0375m^{3}[/tex]
