to view answer.The process of evaluating a formula involves substituting values in for the known or input variable(s) and calculating to determine the value of the unknown or output variable.
Some practice problems follow:
Find the area of a rectangle that has a length of 9.2 cm and width of 3 cm.
Since the area of a rectangle is defined by the formula, $$A = l \cdot w$$
and since $$l = 9.2$$ cm. and $$w = 3$$ cm, we substitute these values in for l and w and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
A = (9.2)(3) \cr
= 27.6{\text{ sq c}}{{\text{m}}^2} \cr} $$
Find the perimeter of a rectangle that has a length of 17.4 inches and a width of 26.5 inches.
Since the perimeter of a rectangle is defined by the formula, $$P = 2l + 2w$$ and since $$l = 17.4{\text{ inches}}$$ and $$w = 26.5{\text{ inches}}$$, we substitute these values in for l and w and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
P = 2\left( {17.4} \right) + 2\left( {26.5} \right) \cr
= 87.8{\text{ inches}} \cr} $$
Determine the area of a circle that has a radius of 4.2 feet.
Since the formula for the area of a circle is$$A = \pi {r^2}$$ and $$r = 4.2$$
feet we substitute this value for r and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
A = \pi {\left( {4.2} \right)^2} \cr
\approx 55.42{\text{ f}}{{\text{t}}^2} \cr} $$
Determine the circumference of a circle that has a radius of 3.24 cm.
Since the formula for the circumference of a circle is $$C = 2\pi r$$ and $$r = 3.24{\text{ cm}}{\text{.}}$$ we substitute this value for r and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
C = 2\pi \left( {3.24} \right) \cr
\approx 20.36{\text{ cm}}{\text{.}} \cr} $$
Determine the surface area of a cube that has a side length of 5.3 yards.
Since the formula for the surface area of a cube is $$SA = 6{s^2}$$ and $$s = 5.3{\text{ yards}}$$ we substitute this value for s and calculate.
Think about it for a moment and then access this link to view answer.
$$\displaylines{
SA = 6{\left( {5.3} \right)^2} \cr
= 168.54{\text{ y}}{{\text{d}}^2} \cr} $$
Determine the volume of a cube that has a side length of 5.3 yards.
Since the formula for the volume of a cube is $$V = {s^3}$$
and s = 5.3 yards we substitute this value for s and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
V = {\left( {5.3} \right)^3} \cr
= 148.877{\text{ y}}{{\text{d}}^3} \cr} $$
Determine the volume of a sphere that has a radius of 6.1 inches.
Since the volume of a sphere can be determined using the formula $$V = \frac{4}
{3}\pi {r^3}$$ and $$r = 6.1{\text{ inches}}$$, we substitute this value for r and calculate.
Think about it for a moment and then access this link to view answer.
$$\eqalign{
SA = 4\pi {\left( {6.1} \right)^2} \cr
\approx 467.59{\text{ i}}{{\text{n}}^2} \cr} $$
Explain the difference between an inch, a square inch, and a cubic inch.
Think about it for a moment and then access this link to view answer.
An inch is a linear measurement that is $$\frac{1}{{12}}th$$ as long as a foot.
A square inch is an area measurement that is a square 1-inch on each side.
A cubic inch is a volume measurement that is a cube 1-inch on each side.