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?

Question

Avery Allen · Accepted Answer

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

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#

Avery Allen · Answer

undefined The shape formed by rotating a right triangle with a hypotenuse of 34 cm and a minor cathetus of 16 cm about the major cathetus is a cone.

To calculate the surface area of the cone, you use the formula $ A = \pi r^2 + \pi r l $, where $ r $ is the radius of the base and $ l $ is the slant height. The radius $ r $ can be found using the Pythagorean theorem, and the slant height $ l $ is the hypotenuse of the original triangle.

To calculate the volume of the cone, you use the formula $ V = \frac{1}{3} \pi r^2 h $, where $ h $ is the height of the cone.

Given the dimensions of the triangle and using the formulas mentioned above, you can calculate the surface area and volume of the resulting cone.