Question

6. The volume of a cube is increasing at a rate of 10 cubic cm/min. How fast is the surface area of the cube increasing when the length of the edge is 30 cm?

Answer #1

Volume of a cube having side length 'a' is given by

The volume of a cube is increasing at a rate of 10 cubic cm/min.

That is

Surface area of the cube is given by

When length of the edge is 30 cm.

That is

**Surface area is increasing at a rate of 1.33 square
cm/min.**

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(1) The volume of a cube is increasing at a rate of 10 cm3/min.
How fast is the surface area increasing when the length of an edge
is 20 cm?
(2) Suppose oil spills from a ruptured tanker and spreads in a
circular pattern. If the circumference of the oil spill increases
at a constant rate of 2 m/s, how fast is the area of the spill
increasing when the radius is 30 m?

each side of a cube is increasing at a rate of 4 cm/s at what
rate is the surface area of the cube increasing when the surface
area of the cube is 486 cm^2

The length of a rectangle is increasing at a rate of 5 cm/s and
its width is increasing at a rate of 4 cm/s. When the length is 15
cm and the width is 6 cm, how fast is the area of the rectangle
increasing?

The volume of a cube is decreasing at the rate of 360cm^3/sec at
the moment its total surface area is 2400cm^2. What is the rate of
change of the length of one edge of the cube at this moment?

The altitude (height) of a triangle is increasing at a rate of 1
cm/min while the area of the triangle is increasing at a rate of 2
square cm per min. At what rate is the base of the triangle
changing when the altitude is 10 cm and the area is 100 square
cm?

a. Each side of a square is increasing at a rate of 2 cm/s. At
what rate is the area of the square increasing when the area of the
square is 49 cm2? cm2/s
b. The length of a rectangle is increasing at a rate of 4 cm/s
and its width is increasing at a rate of 5 cm/s. When the length is
7 cm and the width is 5 cm, how fast is the area of the rectangle
increasing?

The length of a rectangle is increasing at a rate of 8 cm/s and
its width is increasing at a rate of 9 cm/s. When the length is 9
cm and the width is 5 cm, how fast is the area of the rectangle
increasing?

The
altitude of a triangle is increasing at a rate of 2.5 cm/min
while the area the triangle is increasing at a rate of 2.5 cm² per
minute. At what rate is the base of the triangle changing when the
altitude is 8.5 cm and the area is 94 cm² ?

The altitude of a triangle is increasing at a rate of 1 cm/min
while the area of the triangle is increasing at a rate of 2
cm2/min.
At what rate is the base of the triangle changing when the altitude
is 20 cm and the area is 160 cm2?

The altitude of a triangle is increasing at a rate of 1 cm/min
while the area of the triangle is increasing at a rate of 2
cm2/min. At what rate is the base of the triangle
changing when the altitude is 20 cm and the area is 100
cm2?

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