Quiz Problems for Area, Perimeter, Surface Area, Volume

If the formula for the perimeter of a rectangle is P = 2l + 2w, solve for the variable w in terms of P and l.

• w = P - l

• w = (P - 2l) / 2

• w = P / 2l

• w = P + 2l

If the formula for the surface area of a cube is A = 6s^2, solve for the variable s in terms of A.

• s = A / 6

• s = (A / 6)^(1/2)

• s = 6A

• s = sqrt(6A)

In the formula A = lw, solve for the variable w.

• w = A - l

• w = A/l

• w = A + l

• w = A * l

If the formula for the volume of a cylinder is V = πr^2h, solve for the variable h in terms of V and r.

• h = V * πr^2

• h = V - πr^2

• h = V + πr^2

• h = V / (πr^2)

If the formula for the volume of a sphere is V = 4/3πr^3, solve for the variable r in terms of V.

• r = (3V / 4π)^(1/3)

• r = 3V / 4π

• r = (4V / 3π)^(1/3)

• r = 4V / 3π

Each edge of a cube box, s, is decreasing at the rate of 12cm/sec. At what rate is the the total surface area of the cube box changing when the edge of the box is 2cm. (Cube total surface area A=6S²)

• -144 cm²/sec

• 144 cm²/sec

• 288 cm²/sec

• -216 cm²/sec

• -288 cm²/sec

Each edge of a square, s, is decreasing at the rate of 9cm/sec. At what rate is the area changing when the edge of the box is 6cm.(Area of a square A=S²)

• 108 cm²/sec

• 54 cm²/sec

• 18 cm²/sec

• -108 cm²/sec

• -54 cm²/sec

Each edge of a square, s, is increasing at the rate of 10cm/sec. At what rate is the perimeter changing when the edge of the box is 4cm. (Perimeter of a square P=4S)

• 40 cm/sec

• 160 cm/sec

• -160 cm/sec

• 80 cm/sec

Each edge of a cube box, s, is increasing at the rate of 2cm/sec. At what rate is the volume changing when the edge of the box is 5cm.(Volume of a cube V=S³)

• 75 cm³/sec

• 40 cm³/sec

• 150 cm³/sec

• 125 cm³/sec

The radius r of a circle is decreasing at a rate of 12 inches per minute.

Find the rate the area is changing when the radius is 4 inches.

Use A=πr² and leave your answer in terms of π

• 48π in²/min

• 96π in²/mi

• -96π in²/mi

• -192π in²/mi

• 192π in²/mi