Question

The right cylinder is inscribed into the right pentagonal prism with the base edges are 6ft. And the height is 8 ft the volume of the cylinder is

Answer 1

Given:

r =  6ft

h =  8 ft

To find:

V =?

Step-by-step explanation:

A right, pentagonal prism is inscribed in a right circular cylinder where the bases of the prism are inscribed in the bases of the cylinder and the lateral edges of the prism are touching the curved lateral surface of the cylinder.

The perpendicular distance is 6ft.

∴ volume of cylinder = $\frac{1}{2} (5s \times a) h$

                                  = 0.5 × (5 × 6  × 6) × 8

                               V = 2880 $ft^3$

                               

Answer 2

Answer:

428.3 ft^3

Step-by-step explanation:

If you divide circle in five equal parts every part is 360°/ 5=72° ; you have five equal traingle whose their vertexes are on the center of the base of the cylinder ; now draw the one of the height of traingle ; you see a right traingle that has an angle= 72÷2=36°

Tan36=3/R (whose R is the radius of the base and 3= length of one side of pentgon÷2)

R=3/tan36 ; R=4.3

Area of the base of cylinder S=piR^2 ; S=3.14×(3.4)^2 ; S=53.537 sq feet

Volume of cylinder= area of base× height

V=53.537 ×8

V=428.3 feet^3