Question

The coordinates A(0, 0), B(0, 5) and C(3, 0) are graphed and connected together. What 3-dimensional shape will be created when this shape is rotated about the y-axis? Provide an explanation and proof for your answer to receive full credit.

Answer 1

Answer:

The 3-dimensional shape created will be a cone

Step-by-step explanation:

step 1

Plot the points

we have

A(0, 0), B(0, 5) and C(3, 0)

The figure is a right triangle

see the attached figure

so

When this shape is rotated about the y-axis, the 3-dimensional shape created will be a cone

where

AC is the radius of the base of cone

The radius is equal to r=AC=3 units

AB is the height of the cone

The height is h=AB=5 units

BC is the slant height of the cone

Applying Pythagoras Theorem

$BC^{2} =AB^{2} +AC^{2}$

$BC^{2} =5^{2} +3^{2}$

$BC^{2} =34$

$BC=\sqrt{34}\ units$