Surface area of basket ball full of sand

[JUSTaROCK]

Homework Statement

A regulation NCAA basketball is a sphere of radius approximately 12 cm. Grains of Texas beach sand are
approximately spheres of radius 25 μm. If the inside volume of a basketball were completely filled with sand
(assume perfect packing with no empty space) what is the approximate total surface area, in m2, of all of the
sand grains?

Homework Equations

area of circle = pi(r)^2
surface area = 4pi(r)^2
volume = 4pi/3(r)^3
nanometers = 1/10^6 meters
centimeters = 1/10^2 meters

The Attempt at a Solution

I have tried to solve for this by finding the volume of the basketball then finding the surface area of a single grain. I then took the volume of the basket ball and divided it by the area of a single grain to see how many would fit, once i got that number i multiplied it by the surface area of one grain of sand for the total surface area. I made sure to convert all the units to their proper places and amounts but still no luck. Please help i have a final tomorrow and i can't figure this one out i have spent hours on it, thank you.

 

[novop]

Find the volume of the basketball and the volume of a grain of sand, then find how many grains of sand would fit in if they were perfectly packed. Find the surface area of a single grain... missing the last step... good enough?

 

[JUSTaROCK]

so your saying divide the volume of the basketball by the volume of a grain? then multiply that by the surface area of a grain?

 

[novop]

Yep. Make sense?

 

[RTW69]

Find how many grains of sand will fill the basketball (you need to find the volume of each). Find the surface area of a grain of sand. Multiply.

 

[JUSTaROCK]

Thank you so much guys really appreciate it