Question

Calculate the surface area and the volume of a sphere with radius 12ft.
A. $V = 6236.56f{t^3}$ and $A = 1808.64f{t^2}$
B. $V = 7234.56f{t^3}$ and $A = 1808.64f{t^2}$
C. $V = 6236.56f{t^3}$ and $A = 2808.64f{t^2}$
D. $V = 7134.56f{t^3}$ and $A = 1808.64f{t^2}$

Answer 1

Hint: We will use the formula for surface area and volume of a sphere to find out the respective values for the given sphere with radius 12ft.

Complete step by step answer:
Now, Surface area of a Sphere as we know is given as:

$SA = 4\pi {r^2}$, where SA is the Surface Area, $\pi $ is a constant with value $3.14$ and r is the radius(12 ft.)
So, according to the question the radius given to us is = 12ft,
Then, the SA will be calculated as follows:
$ SA = 4\pi {r^2} \\
   = 4 \times \dfrac{{22}}{7} \times {\left( {12} \right)^2} \\
   = \dfrac{{4 \times 22 \times 12 \times 12}}{7} \\
   = 1808.64f{t^2} \\ $
Next we need to find the volume of the sphere.
Now, volume of the sphere is given as:
$V = \dfrac{4}{3}\pi {r^3}$ where, Vis the volume, $\pi $ is a constant with value $3.14$and r is the radius(12 ft.)
So, according to the question the radius give to us is = 12ft,
Then, V will be calculated as follows:
$ V = \dfrac{4}{3}\pi {r^3} \\
   = \dfrac{4}{3} \times 3.14 \times {\left( {12} \right)^3} \\
   = \dfrac{{4 \times 3.14 \times 12 \times 12 \times 12}}{3} \\
   = 7234.56f{t^3} \\ $

Therefore, the Surface Area and Volume of the given sphere with radius 12ft is $1808.64f{t^2}$and $7234.56f{t^3}$..

Note:
While doing mensuration problems one must see units related to terms given. If there are different units then the first step is to make their units same and then form different equations as per the given condition and then solve them together to find the required solution of the problem. Also use of $\pi$ as $3.14$ instead of $\dfrac{22}{{7}}$ can lead to different answers, so one must take the value of $\pi$ mentioned in the given problem.