Answer:
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)
