A right triangle with a hypotenuse of 34 cm and a minor cathetus 16 of cm rotates 360° about the major cathetus. What shape does it form? How do you calculate the surface area and volume of the shape it forms?

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Answer 1 · 2016-12-03T04:34:18

conical shape. Surface area #SA= 800pi#, Volume #V=2560pi#

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In the diagram above, #l# is the hypotenus, #r# is the minor cathetus, and #h# is the major cathetus.

Surface area #SA=pir^2+pirl#
Given #l=34, and r=16#
#=> SA=pi*16^2+pi*16*34=pi*(16^2+16*34)#
#=> SA= 800pi=2513.27#

Volume #V=pir^2(h/3)#
#h=sqrt(l^2-r^2)=sqrt(34^2-16^2)=30#
#=> V =pi*16^2*(30/3) = 2560pi =8042.48#