Question

A rectangular prism is truncated removing 30% of its height. The original height of the prism was 100 cm and it has a length of 6 cm and a width of 12 cm. What is the volume of the truncated prism?

Answer 1

Height is cut by 30%

So new height became:

\[New \; Height = H - \frac{30}{100}H = \frac{7}{10}H\]

Answer 2

So:

\[Volume = 6 \times 12 \times \frac{7}{10}H\]

Previous volume was :

\[100 = L \times B \times H\]

\[H = \frac{100}{72}\]

Answer 3

Put it in the new volume we got..

Answer 4

\[Volume = 6 \times 12 \times \frac{7}{10}H \implies 72 \times \frac{7 \times 100}{ 10 \times 72} \implies 70\]

Answer 5

This stuff is so rough.

Answer 6

Getting @Mastercat

Answer 7

Rough ??

But I have used equation editor instead of drawing..

Ha ha ha..

Answer 8

Let us start from the start...

Answer 9

I miss algebra... so much easier.

Answer 10

Volume given was : 100 L = 6 and H = 12

Use volume formula and find previous H..

\[Volume = 6 \times 12 \times H \implies 100 = 72 \times H\]

Find H from it by dividing 72 both the sides..

\[H = \frac{100}{72}\]

Getting till here @Mastercat

Answer 11

Sorry W = 12 and not H in the first line I have written wrong...

Answer 12

Now this we got was previous Height that is 100/72..

Now after truncating it gets reduced by 30%

Answer 13

\[\frac{100}{72} - \frac{30}{100} \times \frac{100}{72} = \frac{100}{72} \times \frac{70}{100} \implies \frac{70}{72}\]

This is the new height after truncation..

Answer 14

Now again use the volume formula;

\[Volume = 6 \times 12 \times \frac{70}{72} \implies 70\]

Answer 15

But we have to find the volume of truncated portion and not the volume of prism that is left after truncation..

So,

Subtract both the volumes:

\[\large Volume(truncated) = 100 - 70 \implies \color{blue}{30}\]

Answer 16

http://www.youtube.com/watch?v=bXScgXleLX8&feature=related = My Brain

Answer 17

My internet always goes like an ant...

I will see it some other day...

Answer 18

Sorry... Just so complex. Im looking at it.