Unit 2 Lesson 16

There are many cylinders with a volume of  $144\pi$  cubic inches. The height  $h\left(r\right)$  in inches of one of these cylinders is a function of its radius  $r$  in inches where  $h\left(r\right)=\frac{144}{r^2}.$  What is the height of one of these cylinders if its radius is 2 inches?

There are many cylinders with a volume of  $144\pi$  cubic inches. The height  $h\left(r\right)$  in inches of one of these cylinders is a function of its radius  $r$  in inches where  $h\left(r\right)=\frac{144}{r^2}.$  What is the height of one of these cylinders if its radius is 3 inches?

There are many cylinders with a volume of  $144\pi$  cubic inches. The height  $h\left(r\right)$  in inches of one of these cylinders is a function of its radius  $r$  in inches where  $h\left(r\right)=\frac{144}{r^2}.$  What is the height of one of these cylinders if its radius is 6 inches?

The surface area $S\left(r\right)$  in square units of a cylinder with a volume of 18 cubic units is a function of its radius  $r$  in units where  $S\left(r\right)=2\pi r^2+\frac{36}{r}.$  What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units.

•  $6\pi+12$  square units

•  $9\pi+12$  square units

•  $12\pi+12$  square units

•  $18\pi+12$  square units

Han finds an expression for $S\left(r\right)$  that gives the surface area in square inches of any cylindrical can with a specific fixed volume, in terms of its radius  $r$  in inches. This is the graph Han gets if he allows  $r$  to take on any value between  $-1$  and  $5.$  What would be a more appropriate domain for Han to use instead?

•  $r<0$  

•  $r<2$  

•  $r>0$  

•  $r>2$  

Han finds an expression for $S\left(r\right)$  that gives the surface area in square inches of any cylindrical can with a specific fixed volume, in terms of its radius  $r$  in inches. This is the graph Han gets if he allows  $r$  to take on any value between  $-1$  and  $5.$  What is the approximate minimum surface area for the can?

The polynomial function $p\left(x\right)=x^4+4x^3-7x^2-22x+24$  has known factors of  $\left(x+4\right)$  and  $\left(x-1\right).$  Rewrite  $p\left(x\right)$  as the product of linear factors.

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Which polynomial has $\left(x+1\right)$  as a factor?

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