Question

What is the surface area and volume of a golf ball with a diameter of \[1.7\] inches?

Answer 1

Hint: Golf ball is in the shape of a sphere. From the mensuration formulas we know surface area of sphere is \[4\pi {{r}^{2}}\] and volume of sphere is \[\dfrac{4}{3}\pi {{r}^{3}}\] where \[r\] is the radius of sphere. Now we will use these basic formulas to find the surface area and volume of the golf ball. Standard value of \[\pi \] is \[3.14\].

Complete step by step solution:
From the given question we were given the diameter of a golf ball as \[1.7\] inches. With that information we have to find the surface area and volume of the golf ball.
Let us take diameter of golf ball as \[d\]
From given diameter of golf ball is \[1.7\]inches
\[\Rightarrow d=1.7\]inches
Now we have to convert diameter into radius
We know from basic concept, diameter is two times of radius.

\[\Rightarrow d=2r\]
\[\Rightarrow 1.7=2\times r\]
\[\Rightarrow r=0.85\]inches.
where, \[r\] is the radius of the golf ball.
Now let us try to calculate surface area of golf ball
We know surface area of sphere is \[4\pi {{r}^{2}}\]
Let us consider surface area as \[s\]
So,\[s=4\pi {{r}^{2}}\]………………..(1)
Now put \[r=0.85\] in equation (1)
\[\Rightarrow s=4\times \pi \times {{\left( 0.85 \right)}^{2}}\]…………….(2)
The value of \[{{\left( 0.85 \right)}^{2}}\] is 0.72 inches. Now put this value in equation (2)
\[\Rightarrow s=4\times 3.14\times 0.72\]\[i{{n}^{2}}\]
On simplification we get
\[\Rightarrow s=9.04\]\[i{{n}^{2}}\]
Now let us try to calculate the volume of golf ball
We know volume of sphere is \[\dfrac{4}{3}\pi {{r}^{3}}\]
Let us consider the volume as \[v\]
\[\Rightarrow v=\dfrac{4}{3}\pi {{r}^{3}}\]………………….(3)
Now put \[r=0.85\]in equation (3)
Now equation (3) becomes as
\[\Rightarrow \dfrac{4}{3}\times \pi \times {{\left( 0.85 \right)}^{3}}\]…………………(4)
We know value of \[{{\left( 0.85 \right)}^{3}}\] as \[0.614\].so put \[{{\left( 0.85 \right)}^{3}}=0.614\] in equation (4).
\[\Rightarrow v=\dfrac{4}{3}\times 3.14\times 0.614\] \[i{{n}^{3}}\]
On simplification we get
\[\Rightarrow v=2.570\] \[i{{n}^{3}}\]
Now we can conclude that surface area of golf ball as \[9.04\] \[i{{n}^{2}}\]and volume of golf ball as \[2.570\] \[i{{n}^{3}}\]

Note: Students should know the formulas of surface area and volume of sphere. Students should be careful while doing calculations because even a small calculation error can lead to big errors in the final answer while finding the surface area and volume of the golf ball.