Question

A sphere of radius 2x m has an area of ​​152.4 m2 and a volume of 360.9 m3. How much will the area and volume of another sphere of radius r = 3x measure?
I will do anything if you tell me this

Answer 1

Answer:

$V = 1218.0375m^{3}$

$A = 342.9m^{2}$

Step-by-step explanation:

Area:

$A =$ π $r^{2}$

$152.4 =$ π $(2x)^{2}$       *Square 2x*

$152.4 =$ π $4x^{2}$          *Divide by π*

$48.510 = 4x^{2}$           *Divide by 4*

$12.128 = x^{2}$             *Square root*

$\sqrt{12.128} = x$           *Solve*

x ≈ 3.482

Now take the same equation but replace 2x with 3x

$A =$ π $r^{2}$

Now replace x with 3.482 and solve for area.

$A = 342.9m^{2\\}$

Volume:

$V = \frac{4}{3}$ π $r^{3}$               *Insert variables*

$360.9 = \frac{4}{3}$ π $(2x)^{3}$     *Cube 2x*

$360.9 = \frac{4}{3}$ π $(8x^{3})$     *Multiply $\frac{3}{4}$ on both sides*

$270.675 =$ π $(8x^{3})$    *Divide by π*

$86.159 = 8x^{3}$           *Divide by 8*

$10.770 = x^{3}$             *Cube root*

$\sqrt[3]{10.770} = x$            *Solve*

x ≈ 2.208

Now take the same equation but replace 2x with 3x

$V = \frac{4}{3}$ π $(3x)^{3}$    

Now replace x with 2.208 and solve for volume.

$V = 1218.0375m^{3}$