Question

The cylinder and rectangular prism below both have a height of 9 inches and a volume of 452.39in^3.

Answer 1

Answer:

a) Area of base of cylinder = $=50.0346 in^2$

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 =$\pi r^2 h$

Height of cylinder = 9 inches

We are given that the volume of cylinder is $452.39 in^3.$

$\pi r^2 h =452.39\\\frac{22}{7} r^2(9)=452.39\\r=\sqrt{\frac{452.39 \times 7}{22\times 9}}\\r=3.99$

Area of base of cylinder = $\pi r^2= \frac{22}{7} \times (3.99)^2=50.0346 in^2$

Volume of prism = $Length \times Breadth \times height$

Height of prism = 9 inches

Volume of prism = $452.39 in^3$

So,$Length \times Breadth \times height =452.39$

$Length \times Breadth \times 9=452.39\\ Length \times Breadth =\frac{452.39}{9}$

Area of base of prism = 50.265

Width of prism = 5.8

So, $Length \times 5.8 \times 9 =452.39\\Length = \frac{452.39}{5.8 \times 9 }\\Length =8.66647$

a) Area of base of cylinder = $=50.0346 in^2$

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