Question

From a piece of paper, Sam cuts a rectangle with a length that is 2 inches (in.) longer than the width. He tapes a straw to the long side of the rectangle. Holding the straw horizontally at one end, he twirls it, causing the rectangle to create the image of a solid figure. Which statement best describes the solid figure?

a) A rectangular prism with a volume of w^{2\ }+\ 4w\ \ +4\ in^3w 2 +4w+4in 3 where w represents the width of the rectangle.
b) A rectangular prism with a volume of w^3+4w^{2\ }+4w\ in^3 w 3 +4w 2 +4win 3 where w represents the width of the rectangle.
c) A cylinder with a volume of \pi\left(w^3+2w^2\right)in^3π(w 3+2w 2)in 3 where w represents the width of the cylinder.
d) A cylinder with a volume of \frac{\pi\left(w^3+2w^2\right)}{3}in^33π(w 3+2w 2 ) in 3 where w represents the width of the cylinder.

Answer 1

c)A cylinder with a volume of π(w³ +2w² )in³

where w represents the width of the cylinder.

Explanation:

A cylinder with a volume of π(w³ +2w² )in³

where w represents the width of the cylinder.

The volume of a cylinder is given by V=Bh or V=πr²h

where B is the area of the base and h is the height of the cylinder.

V=πr²h-------equation1

V= π(w³ +2w² )--------- equation2

Comparing equation 1 and equation 2

πr²h=π(w³ +2w² )

r²h=(w³ +2w² )

r²h= w²(w +2 )

Taking w² common leaves w+2 which gives the height or length of the cylinder.

Therefore radius = width and height = length which gives the volume of the cylinder.