# Total Surface Area of one piece of a sphere. Help :s

• Jun 4th 2010, 03:13 PM
Kekemapa93
Total Surface Area of one piece of a sphere. Help :s
I don't know how to do this, I tried and got it wrong. I know the answer but can someone please take me through the steps. It's for the calculator paper.

The volume of the sphere is 5000cm cubed.
The radius of the sphere is 10.6cm to one decimal place.
The sphere is sliced through the centre to make 20 identical pieces.

Calculate the total surface area of one of the pieces.

How do I do this? Thanks in advance :)
• Jun 4th 2010, 05:38 PM
Sudharaka
Quote:

Originally Posted by Kekemapa93
I don't know how to do this, I tried and got it wrong. I know the answer but can someone please take me through the steps. It's for the calculator paper.

The volume of the sphere is 5000cm cubed.
The radius of the sphere is 10.6cm to one decimal place.
The sphere is sliced through the centre to make 20 identical pieces.

Calculate the total surface area of one of the pieces.

How do I do this? Thanks in advance :)

Dear Kekemapa93,

Is this a hollow sphere or a solid sphere?
• Jun 5th 2010, 05:14 AM
Kekemapa93
It's solid :)
• Jun 5th 2010, 06:36 AM
sa-ri-ga-ma
Volume of the sphere is 5000 cm^3

The surface area = 4πr^2

The top surface area each section is 4π^2/20 cm^2

The slices will be identical if the perimeter of the top surface form a square.

Length of the arc of each side of the top surface of the slice s = 2πr/20.

Area of each sector = $\displaystyle \frac{1}{2}*(r^{2}\theta)$

s = rθ or θ = s/r

Total area of the sectors = 4*$\displaystyle \frac{1}{2}r^2*\frac{s}{r}$

Now find total surface area of the slice.
• Jun 5th 2010, 06:59 AM
Kekemapa93
Thank you. I know how to do it now. I thought a question like this would come up on my test on Monday and I didn't understand :) Thanks again.
• Jun 5th 2010, 10:37 AM
earboth
Quote:

Originally Posted by Kekemapa93
I don't know how to do this, I tried and got it wrong. I know the answer but can someone please take me through the steps. It's for the calculator paper.

The volume of the sphere is 5000cm cubed.
The radius of the sphere is 10.6cm to one decimal place.
The sphere is sliced through the centre to make 20 identical pieces.

Calculate the total surface area of one of the pieces.

How do I do this? Thanks in advance :)

If I understand your question correctly the solid has the form of a kind of wedge with one curved surface and 2 plane sides. (see attachment)

1. The curved side has an area of:

$\displaystyle a_1=\dfrac{4 \pi r^2}{20}$

2. The two plane sides form a complete circle with radius r:

$\displaystyle a_2 = \pi r^2$

3. The complete surface is then $\displaystyle a_1 + a_2$
• Jun 5th 2010, 12:13 PM
Kekemapa93
^I did that. My calculator was wrong I think though. Thanks to both of you for answering my question.