Question

How do I do question 11? Please help me thank you

Answer 1

Given

• length, width, and height of a cuboid are x, x, and 2x, respectively
• the cuboid's surface area is 129.6 cm²
• dx/dt = 0.01 cm/s

Find

• dV/dt for the given conditions

Solution

The equation for surface area can be written

... A = 2(LW +H(L +W))

Substituting the given values gives an equation that we can solve for x

... 129.6 = 2(x·x +2x(x +x)) = 10x²

... x = √(129.6/10) = 3.6 . . . . . . . cm

The equation for volume can be written

... V = LWH

Substituting the given values gives an expression for volume in terms of x.

... V = x·x·2x = 2x³

Then the rate of change of volume is

... dV/dt = 6x²·dx/dt

... dV/dt = 6·(3.6 cm)²·(0.01 cm/s)

... dV/dt = 0.7776 cm³/s