Answer:
a) Area of base of cylinder = [tex]=50.0346 in^2[/tex]
Area of base of prism = 50.265 sq.in.
b)Radius of cylinder = 3.99 in
c)If the rectangular prism has a width of 5.8 inches so. length is 8.66 in
Step-by-step explanation:
Volume of cylinder =[tex]\pi r^2 h[/tex]
Height of cylinder = 9 inches
We are given that the volume of cylinder is [tex]452.39 in^3.[/tex]
[tex]\pi r^2 h =452.39\\\frac{22}{7} r^2(9)=452.39\\r=\sqrt{\frac{452.39 \times 7}{22\times 9}}\\r=3.99[/tex]
Area of base of cylinder = [tex]\pi r^2= \frac{22}{7} \times (3.99)^2=50.0346 in^2[/tex]
Volume of prism = [tex]Length \times Breadth \times height[/tex]
Height of prism = 9 inches
Volume of prism = [tex]452.39 in^3[/tex]
So,[tex]Length \times Breadth \times height =452.39[/tex]
[tex]Length \times Breadth \times 9=452.39\\ Length \times Breadth =\frac{452.39}{9}[/tex]
Area of base of prism = 50.265
Width of prism = 5.8
So, [tex]Length \times 5.8 \times 9 =452.39\\Length = \frac{452.39}{5.8 \times 9 }\\Length =8.66647[/tex]
a) Area of base of cylinder = [tex]=50.0346 in^2[/tex]
Area of base of prism = 50.265
b)Radius of cylinder = 3.99 in
c)If the rectangular prism has a width of 5.8 inches so. length is 8.66 in
