Question

What is the surface area and volume of a bowling ball with a diameter of 8.5 inches?

Answer 1

`color(blue)("Volume"=227.01` `color(blue)("in"^3` `and` `color(indigo)("Surface area"=321.62` `color(indigo)("in"^2`

Explanation:

We use these formulas to calculate the volume and surface area.
(Assume the bowling ball does not have a holes)

As, the bowling ball is a sphere.So, we use

`color(blue)("Volume of the sphere"=4pir^2`

`color(indigo)("Surface area of sphere"=4/3pir^3`

Where,

`color(orange)(r="radius"`

`color(orange)(pi=22/7`

We know that the diameter of the ball is `8.5`.So the radius will be,

`8.5/2=4.25`

`"(As the radius is half the diameter)"`

Let's calculate

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Volume"`

`rarrcolor(blue)(4pir^2`

`rarrcolor(blue)(4*22/7*4.25^2`

`rarrcolor(blue)(88/7*18.06`

`rarrcolor(blue)(12.57*18.06`

`rArrcolor(green)(227.01` `color(green)("in"^3`

`color(white)(45`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(white)(5)color(indigo)("Surface area"`

`rarrcolor(indigo)(4/3pir^3`

`rarrcolor(indigo)(4/3*22/7*4.25^3`

`rarrcolor(indigo)(88/21*76.76`

`rarrcolor(indigo)(4.19*76.76`

`rArrcolor(green)(321.62` `color(green)("in"^2`

`color(white)(45`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`:.color(blue)("Volume"=227.01` `color(blue)("in"^3` `and` `color(indigo)("Surface area"=321.62` `color(indigo)("in"^2`