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?

1 Answer
Dec 3, 2016

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

Explanation:

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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