Surface Area/Volume Problem

Question

A Chocolate Jelly Bean manufacturer decided to produce Jelly Bean Balls(spheres) coated in chocolate. The machine produces 2.5m^3 of Jelly Bean and then splits it into 100000 balls and passes them to another machine to be coated in 2ml of chocolate.

Find: a) The radius of each ball(with and without chocolate)

b) Find the total volume of chocolate needed to cover all Jelly Bean Balls

I've attempted to find the volume of one ball but attempts have proved fruitless. — Mark Zakhem, May 31 '13 at 23:47
What is the volume of a ball? What is the radius so the the sum of the volumes of $100000$ would be $2.5$ — Sigur, May 31 '13 at 23:51
So you are taking 2.5 m^3 of Jelly Bean and DIVIDING it evenly into 100000 pieces, how much is in each piece? — jemmy.bruce, May 31 '13 at 23:54

score 0 · Answer 1 · answered May 31 '13 at 23:59

0

Hint: Now that you have the volume of one ball, use the formula linking the radius of a sphere to its volume to find the radius. Then find the surface area of the sphere from that formula and the radius you know. The thickness of chocolate is the volume of chocolate divided by this area (very close).

answered May 31 '13 at 23:59

Ross Millikan

374,822

Is the radius without the chocolate 1.81 cm? – Mark Zakhem Jun 01 '13 at 00:06
What is the formula that links? – Mark Zakhem Jun 01 '13 at 00:14
You have $V=\frac 43 \pi r^3$ for the volume, $A=4 \pi r^2$ for the area. I get $0.842$ for the radius. – Ross Millikan Jun 01 '13 at 01:22
That's gotta be wrong – Mark Zakhem Jun 01 '13 at 08:46
I keep getting 1.81 – Mark Zakhem Jun 01 '13 at 08:47
I think you are doing 25÷4÷3÷π and then the cube root of that whole answer instead of doing 25÷4/3(as a fraction) ÷π and a cube root of that – Mark Zakhem Jun 01 '13 at 08:51
You are correct. I dropped the decimal point. – Ross Millikan Jun 01 '13 at 15:12

score 0 · Answer 2 · answered Jun 01 '13 at 00:07

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Convert 2ml to m^3 and add it to the volume of small jelly and equate it with 4/3*pi*r^3 to find r after coating.

Total volume is simply no. Of jelly balls * vol. Of chocolate needed for one jelly.

answered Jun 01 '13 at 00:07

Rohinb97

1,702

Surface Area/Volume Problem

2 Answers2