Final answer:
The value of 'h' is 8 cm.
Step-by-step explanation:
To find the value of 'h', we need to find the sum of all the given numbers and subtract it from the sum of the other numbers. The sum of 7 cm, 15 cm, 12 cm, 5 cm, and 13 cm is 7 + 15 + 12 + 5 + 13 = 52 cm. The sum of all the numbers including 'h' is 52 + h.
Since the mean of all the numbers is 10 cm, we can set up an equation:
(52 + h) / 6 = 10 cm
To solve for 'h', we first simplify the equation:
52 + h = 10 * 6
52 + h = 60 cm
Then, we isolate 'h' by subtracting 52 from both sides of the equation:
h = 60 - 52
h = 8 cm