Question

The length of each side of a metal cube increases at the rate of 0.025cms' when heated. Find the rate of increase in cm²s¯¹ of the total surface area of the cube, when the length of each side is 6cm.

Plssss I really need this submission due tomorrow by 6 am​

Answer 1

3.06 cm^2/sec

Explanation:

Since the shape is a cube, all sides have equal lengths, 6 cm The rate of increase of 0.025cm/s [Note: I assume the unit should be cm/s, not cms'].

See the attached spreadsheet calculation. Starting at time = 0 sec, the initial area is 36 cm^2. Each second adds 0.025 cm to each side length,.

We can express this change in length as an equation:

Initial Length (6cm) + (x seconds)*(0.025 cm/s)

So for 10 second, l = 6 cm + 0.25cm or 6.25cm

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The area is also changing with time. At 0 seconds, the area is (6cm)^2 or 36 cm^2. At 10 seconds, the area is (6.25cm)*(6.25cm) or 39.06 cm^2.

The area increased from 36 cm^2 to 39.06 cm^2 in 10 seconds. That is a change rate of ((39.06 - 36 cm^2)/(10 sec):

((39.06 - 36 cm^2)/(10 sec)

((3.06 cm^2)/(10 sec)

3.06 cm^2/sec