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.

Guest Aug 28, 2018

#1**+1 **

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

CPhill
Aug 28, 2018

#3**+1 **

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!!!

CPhill
Aug 28, 2018