Find the height of a straight circular truncated cone, the base radii of which are 6√2 cm, 11√2 cm

Find the height of a straight circular truncated cone, the base radii of which are 6√2 cm, 11√2 cm, and the generatrix is 7√2 cm.

Given: truncated cone, r = 6√2 cm, R = 11√2 cm, l = 7√2 cm.
Find: h.
Solution:
a = R- r = 11√2 cm-6√2 cm = 5√2 cm.
Consider a right-angled triangle with a leg a = 5√2 cm and a hypotenuse l = 7√2 cm. The second leg b will be equal to the height of the truncated cone.
By the Pythagorean theorem:
l ^ 2 = a ^ 2 + b ^ 2,
b ^ 2 = l ^ 2-a ^ 2,
b ^ 2 = (7√2) ^ 2- (5√2) ^ 2,
b ^ 2 = 48,
b = 4√3.
Answer: 4√3 cm.