# Math Help - Finding volume and surface area of right prism

1. ## Finding volume and surface area of right prism

How to find the volume and surface area of right prisms in the attachments ?

2. $\mbox{Volume} = \mbox{Base} * \mbox{Height} * \mbox{Depth}$

$\mbox{Surface area (Of each face)} = \mbox{Base} * \mbox{Height}$

Divide the prisms into many simpler shapes (eg. rectangular cubes for volume, or rectangles/squares for surface area) so it is easier to work with and find the surface area and volume seperately. Afterwards add them together to get the final surface area or volume of each prism.

For the wedge, use:

$\mbox{Volume} = \dfrac{\mbox{Base} * \mbox{Height} * \mbox{Depth}}{2}$ for the volume

$\mbox{Surface area (Of each triangular face)} = \dfrac{\mbox{Base} * \mbox{Height}}{2}$ for the surface area of the triangular faces

3. I think I'll put more detail for the volume of a prism.

$Volume\ =\ Area\ of\ Cross\ Section\ \times\ Depth$

You need to first identify the cross section of the solid, the area which 'repeats' itself through the solid. In the first one, the cross section is a cross, in the second, it's this 'L' shape and in the last, it's a right angled triangle. Once you get their cross sectiona; area, you'll be able to find the volume by multiplying it by the depth of the solid.

4. For attachment 1 Volume=12*16*20=3840 ?

and area=12*16=192

Is this the right answer ?

5. Please solve the 1st one with ur details so that i can understand.

6. First one:

$\mbox{Total Volume} = (4 * 5 * 3) + (4 * 5 * 3) + (14 * 3 * 4)$

$\mbox{Total Volume} = 288~ \mbox{units}^3$

$\mbox{Surface Area} = (5*4*(8)) + (4*4*(2)) + (4*3*(4)) + (5*3*(8))$ (The single numbers in brackets () are how many faces of each there are.)

$\mbox{Surface Area} = 360~\mbox{units}^2$

7. The area of the cross can be obtained by dividing the cross into 5 parts; 4 rectangles and 1 central square.

Each rectangle has area 5*4 = 20.
Area of 4 rectangles = 20*4 = 80.
Area of central square = 4*4 = 16.
Total area of cross section = 16 + 80 = 96.

Volume of Prism = 96 x 3 = 288 units^3

8. Very difficult question to understand.

9. Unit^2 or unit^3 ?

10. Oh, sorry, a typo from my part. It's units^3

Here is a picture to help you understand. The rectangles are reddish and the central square is grey.