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I am confused by these questions. I need to find the volume of each one but I'm having a hard time. Please help! Thank you.

32) A prism 7 cm tall with a right triangle for a base with side lengths 6 cm, 8 cm, and 10 cm.

47) A pentagonal prism 6 ft tall with a regular base measuring 12 ft on each edge and an apothem of length 8.3 ft.

51) A pentagonal prism 9 mi tall with a regular base measuring 11 mi on each edge and an apothem of length 7.6 mi.

Aug 28, 2018

#1
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32) A prism 7 cm tall with a right triangle for a base with side lengths 6 cm, 8 cm, and 10 cm.

You may not recognize this...but the base forms a "Pythagorean"  right triangle  with legs  of  6 and 8  cm

The area of a right triangle is  (1/2)  ( product of leg lengths)

So...the area of the base   = (1/2) (6 * 8 ) = (1/2) 48  = 24 cm^2

And the volume of the prism is just the   base area  x  height =   24  x  7  =   192 cm^2   Aug 28, 2018
#2
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Thank you so much!

I think I worked that last two out but I'm not confident in my answers. The answer I got for 47 is 1494 ft and the answer that I got for 51 is 1881 mi. Are these correct? Sorry.

Guest Aug 28, 2018
#3
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47) A pentagonal prism 6 ft tall with a regular base measuring 12 ft on each edge and an apothem of length 8.3 ft.

We will have  5congruent triangles forming the base...the height is 8.3 ft and the base =  12 ft

So...the base area  is  5*  (1/2) (8.3) * ( 12) =  249  ft^2

And the volume is  base area x height  =   249 * 6  =   1494  ft^3    CORRECT  !!!

So  51 is similar....the volume is  9 *  5(1/2)(11) ( 7.6)  =   1881  (miles??)^3....that's a  big prism!!!!...LOL!!!   Aug 28, 2018
#4
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Great! That helps a lot! Thank you so much for your help! Have a wonderful day/night!

Guest Aug 28, 2018