the sufance area of a cone is pi r (r+sqrt(h^2+r^2)) BOTTOM LEFT

in our question we know that the height is 4 and because it is a right angle triangle using pythagorean theorm we get 4^2+b^2=5^2 16+b^2=25 b^2=9 b=3

so r=3

plug into our formula pi (3)(3+sqrt(4^2+3^2)) and we get 75.4

the volume is pi r^2 * height/3 pi (3)^2 (4/3) = 37.7

As for the picture on the bottom right

the height assuming that the inside is a right angle triangle is 12 because of pythagorean theorm you are correct good job :)

now we use the same formula as above pi r (r+sqrt(h^2+r^2)) and plug in pi(5)(5+sqrt(12^2+5^2)) and get 282.74

314.16 is the volume since we use the same formula as above pi r^2 * height/3 and plugin in pi 5^2 *12/3 which is pi*25*4

now for the top right

volume is base *height which is v=wlh the height is 8 length is 4 and volume is 64

64=8*4*w

64=32*w

64/32=32*w/32

2=w the width is 2 cm

As for the top left

volume =500

base * height and we know that the base is 125 so

500=125h

500/125=125/125*h

4=h

the height is 4 for the prism

hope this helps

Thank you so much for your help.

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