Here is the problem:
A margarine tub has the shape of the frustum of a cone. With the lower base having diameter length 11 cm and the upper base having diameter length 14 cm, the volume of such a container 6 ⅔ cm tall can be determined by using H = 32 ⅔ cm, and h = 26 cm. Find its volume.
Let
R = ¹⁴⁄₂ = 7 r = ¹¹⁄₂ = 5.5 H = 32 ⅔ cm h = 26 cm k = H - h = 6 ⅔
So the solution in the book is using the formula
V = ⅓πR²H - ⅓πr²h
Which is derived from this image:
doing so we have
V = ⅓ π (7 cm)² (32 ⅔ cm) - ⅓ π (5.5 cm)² (26 cm)
V ≈ 852.593 cm³
To check, I used the other formula:
V = ⅓πk (R² + Rr + r²) ; wherein k = H - h
and the result is
V ≈ 822.050 cm³
Why there are different answers, where does the error came from?