Question

The volume of a sphere is 3,500π m3. what is the surface area of the sphere to the nearest square meter

Answer 1

The surface area of a sphere with a volume of 3,500π m3 is approximately 7,400 m2 when rounded to the nearest square meter. This is found by first calculating the radius using the volume of the sphere and then using this radius to compute the surface area.

Step-by-step explanation:

The question asks for the surface area of a sphere given its volume, which is 3,500π m3. To find the surface area, we first need to find the radius of the sphere using the volume formula for a sphere, which is V = 4/3πr3, and then use the radius in the surface area formula, which is A = 4πr2.

Step 1: Use the volume formula to find the radius.
3,500π m3 = (4/3)πr3
To solve for r, we divide both sides by π and then multiply by 3/4:
r3 = (3,500π m3 * 3) / (4π)
r3 = 2,625 m3
Taking the cube root of both sides, we find:
r = 13.75 m

Step 2: Now that we have the radius, we use the surface area formula.
A = 4πr2
A = 4π(13.75 m)2
A = 4π(189.0625 m2)
A = 2,356.1945π m2
To the nearest square meter, A is approximately 7,400 m2.

Answer 2

v=4
`\pi ( r^(3) )/(3)` find r (the radius).

3500=4
`( r^(3) )/(3)`

`(3500x3)/(4) = r^(3)`

r=
`\sqrt[3]{2625}` =13.79 m

A=4
`\pi r^(2)`
A=761
`m^(2)`