Answer:
volume = 798.58 cm³ (nearest hundredth)
surface area = 678.31 cm³ (nearest hundredth)
Step-by-step explanation:
Volume of a cylinder: [tex]V=\pi r^2h[/tex]
Surface area of a cylinder: [tex]SA=2\pi r^2+2\pi rh[/tex]
Circumference: [tex]C=2\pi r[/tex]
(where r is the radius and h is the height)
Given circumference = 56
⇒ [tex]56 = 2\pi r[/tex]
⇒ [tex]r=\dfrac{56}{2\pi }=\dfrac{28}{\pi }[/tex]
[tex]V=\pi \left(\dfrac{28}{\pi}\right)^2 \times3.2=\dfrac{2508.8}{\pi}=798.58 \textsf{ cm}^3 \textsf{ (nearest hundredth)}[/tex]
[tex]SA=2\pi \left(\dfrac{28}{\pi}\right)^2+56 \times3.2=\dfrac{1568}{\pi}+179.2=678.31 \textsf{ cm}^3 \textsf{ (nearest hundredth)}[/tex]
