A container of yogurt has the shape of the frustrum of a cone. With the lower...

A container of yogurt has the shape of the frustrum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H ?? 30 cm and h ?? 22.5 cm. Find its volum

Expert Solution

Height of frustum of a cone = h = 7.5 cm
Radius of lower end = r = diameter/2= 6cm/2= 3 cm
Radius of upper end = R = diameter/2= 8cm/2= 4 cm
Volume of frustum of cone V = (?h) / 3 x (R^2 + Rr + r^2)
                                      V = (?7.5) / 3 x (16 + 12+ 9)
                                      V = 7.85375 x 37
                                      V = 290.58875 cm3
if height of frustum is 30cm

  V = (?h) / 3 x (R^2 + Rr + r^2)
                                      V = (?30) / 3 x (16 + 12+ 9)
                                      V = 31.415 x 37
                                      V = 1162.355 cm3

if height of frustum is 22.5cm

  V = (?h) / 3 x (R^2 + Rr + r^2)
                                      V = (?22.5) / 3 x (16 + 12+ 9)
                                      V = 23.561 x 37
                                      V = 871.766 cm3

milcah answered 1 year ago

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