Question

Find the total surface area and volume of the object shown in the picture round to the nearest hundredth as needed

Answer 1

We must find the total surface area and volume of the object, this object is a sphere, for this, we use the equations of area and volume of a sphere:

`\begin{gathered} A_S=4\pi\cdot r^2 \\ V_S=(4\pi)/(3)\cdot r^3 \end{gathered}`

In the information we are given we have that the diameter of the sphere is 2.2'', remember that the radius is equivalent to half the diameter so our radius would be as follows:

`\begin{gathered} r=(d)/(2) \\ r=(2.2)/(2) \\ r=1.1 \end{gathered}`

Now, we replace the radius in the equations and solve the area and volume of this object:

`\begin{gathered} A_S=4\pi\cdot(1.1)^2 \\ A_S=(121)/(25)\pi \\ A_S=15.2 \end{gathered}`
`\begin{gathered} V_S=(4\pi)/(3)\cdot(1.1)^3 \\ V_S=5.5752 \\ V_(S\cong)5.58 \end{gathered}`

In conclusion, the surface area is 15.2 square inches and the volume is 5.58