## cbrusoe 3 years ago The figure below shows two similar right triangular prisms. Two right triangular prisms, labeled Prism A and Prism B are shown. The lengths of the legs of the base of Prism A are 6 and 8 and the height of Prism A is 8. The lengths of the cooresponding legs of Prism B are 10.5 and 14. What is the volume of Prism B rounded to the nearest hundredth cubic unit? Answer 367.50 643.13 808.50 1,286.26

1. Hero

Where's the figure?

2. cbrusoe
3. hoblos

the ratio of similarity is 14/8 =1.75 so the height of Prism B = 8*1.75 = 14

4. cbrusoe

im still kinda lost what do i do next to fin the volume of b?

5. Hero

\[V_{prism} = Bh\] where B = area of the base In this case, the first prism has Area of base = (6x8)/2 = (48/2) = 24 Height = 10 Volume = Bh = (24)(10) = 240 the second prism has Area of base = (10.5 x 14)/2 = 73.5 Height = 17.5 Volume = Bh = (17.5)(73.5) = 1286.25

6. cbrusoe

oh ok got it! thanks!

7. Hero

@hoblos found the corect ratio, but not the correct height

8. hoblos

actually a didnt look at the figure.. i worked on the given where the height of A is said to be 8!! but if we look at the figure we see it is 5 ( not 10 @Hero ) so actually the final answer is half what Hero got.. it is 643.13

9. Hero

Had you posted the complete solution @hoblos people would clearly see your reasoning and not have to second-guess your approach. I acknowledge my mistake even though I didn't see the figure, but I at least attempted a completed solution which OS encourages

10. cbrusoe

thank-you both for your help both of you helped me and i thank-you guys for that =)

11. hoblos

you did the reasoning @Hero and it was a good brief one.. what was needed is just dividing your answer by 2 and i dont think that more explanation is needed

12. Hero

You posted the ratio of similarity initially, but a complete solution would have been more useful or at least guiding the student to an answer. Not arguing, just making a suggestion.

13. cbrusoe

while both of you are on here could you help me with this one i got the answer for the last one and i honestly think both answers were usefull A rectangular pyramid and a rectangular prism have bases of the same dimensions as shown below. A rectangular pyramid and a rectangular prism are shown. Both have the length of the rectangular base equal to 7 inches and width of the base equal to 6 inches. The surface area of the rectangular pyramid is 146 square inches. The height of the rectangular prism is the same as the slant height of the pyramid. What is the surface area of the rectangular prism? Answer 292 in2 320 in2 336 in2 438 in2 http://go.flvs.net/courses/1/flvs_57_3641_12676/ppg/respondus/pool_Geom_3641_0700_Subtest_03_15/image0034e5fb4df.jpg

14. hoblos

thats a true point i admit... i gave the height and thought that the only needed after that is just applying a formula which is not that hard!! anyway you did a good job @Hero and thanks for your comments