Chapter 15, Problem 1CR

To determine

To Find: The volume and total surface area of a circular cone.

Answer to Problem 1CR

  $37.7uni{t}^3$ & $1332.4uni{t}^2$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Height of cone}=4\\ \text{Base radius of cone}=3\end{array}$

Formula Used:

  $\begin{array}{l}\text{Pythagoras Theorem}:h^2=b^2+p^2\\ \text{Surface Area}=\pi rl+\pi r^2\\ \text{Volume }=\frac{1}{3}\pi r^{2}h\end{array}$

Calculation:

  $\begin{array}{l}\text{Height of cone}=4\\ \text{Base radius of cone}=3\\ \text{Pythagoras Theorem}:h^2=b^2+p^2\\ \text{Surface Area}=\pi rl+\pi r^2\\ \text{Volume }=\frac{1}{3}\pi r^{2}h\\ l=\sqrt{h^2+b^2}\\ \text{⇒}l=\sqrt{16+9}=\sqrt{25}=5\\ \text{Surface Area}=\pi \times 3\times 5+\pi \times 3^2\\ =\pi \left(15+9\right)\\ =3.14\times 24\\ =1332.4uni{t}^2\\ \text{Volume}=\frac{1}{3}\pi \times 3^2\times 4\\ =3.14\times 3\times 4\\ =37.7uni{t}^3\end{array}$

Conclusion:

Thus the require volume and surface area are $37.7uni{t}^3$ & $1332.4uni{t}^2$ respectively