The volume of a rectangular prism with a cone-shaped hole in it is approximately 163.22 cm^3 What is the height of the cone?

Height of cone = 5 cm

Step-by-step explanation:

Volume of rectangular prism with a cone hole = 163.22 cm³

Volume of rectangular prism - volume of the cone = 163.22 cm³

L*W*H - ⅓πr²h = 163.22

Where,

L = 5 cm

W = 5 cm

H = 7 cm

r = ½(3) = 1.5 cm

h = ?

Plug in the values into the equation and solve for h (height of the cone)

5*5*7 - ⅓*π*1.5²*h = 163.22

175 - 2.36*h = 163.22

-2.36*h = 163.22 - 175

-2.36*h = -11.78

Divide both sides by -2.36

-2.36*h/-2.36 ° -11.78/-2.36

h = 4.99152542

h = 5 cm (nearest tenth)

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step-by-step explanation:

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