Question

Question 5) The diameter of a sphere with a surface area of 81 pi square yards. Part b Find the volume of the composite solid. Somehow, I’m getting the wrong answer that’s not matching the key.

Answer 1

Given:

$\begin{gathered} R=4in \\ h=7in \\ H=15in \end{gathered}$

find: volume of the given figure.

Explanation: volume of the composite solid=volume of cone + volume of cylinder .

we know volume of cone is

$\begin{gathered} =\frac{\pi r^2h}{3} \\ =\frac{(3.14)(16)(7)}{3} \\ =117.23in^3 \end{gathered}$

and the volume of the cylinder is

$\begin{gathered} =\pi r^2H \\ =(3.14)(16)(15) \\ =753.6in^3 \end{gathered}$

Hence the volume of the composite solid is

$\begin{gathered} 753.6+117.23 \\ =870.83in^3 \end{gathered}$

(a) given: the surface area of the sphere is 81pi square yards.

find: the diameter of the sphere.

Explanation: we know that the surface area of the sphere is

$\begin{gathered} 4\pi r^2=81\pi \\ r^2=\frac{81}{4} \\ r=\frac{9}{2} \\ r=4.5yards \end{gathered}$

Hence the diameter is equal to twice of the radius

$4.5\times2=9yards$