Chapter 12, Problem 3RP

a

To determine

To calculate : The volume and the total surface are of Cylinder.

Answer to Problem 3RP

The volume and total surface area of the Cylinder are, $\left(V\right)=360{\text{π units}}^3$ and $\left(A\right)=120{\text{π units}}^2$

Explanation of Solution

Given information:

Diameter $d=12\text{ units}$

Height $h=10\text{ units}$

Formula used:

Radius $r=\frac{d}{2}\text{ units}$

  $\begin{array}{l}\text{Volume of Cylinder }\left(\text{V}\right)=\text{π}{r}^2\times h{\text{ units}}^3\\ \text{Surface Area of Cylinder }\left(A\right)=2\text{π}{r}^2+2\text{π}rh{\text{ units}}^2\end{array}$

Calculation:

Radius of Cylinder

  $r=\frac{12}{2}=6\text{ units}$

Volume of Cylinder is,

  $V=\text{π}{r}^2\times h=\text{π}\times 6^2\times 10=\text{π}\times 36\times 10=360\text{π }{\left(\text{units}\right)}^3$

Total Surface Area of the Cylinder is,

  $\begin{array}{c}A=\left(2r^2+2rh\right)\text{π}\\ =\left(2\times 6^2+2\times 6\times 10\right)\text{π}\\ =\left(2\times 36+2\times 60\right)\text{π}\\ =\left(72+120\right)\text{π}\\ =192{\text{π units}}^2\end{array}$

  

b

To determine

To calculate : The volume and the total surface are of Prism.

Answer to Problem 3RP

The volume and total surface area of the Prism are, $\left(V\right)=675{\text{ units}}^3$ and $\left(A\right)=411{\text{ units}}^2$

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Length }\left(l\right)=15\text{ units}\\ \text{Breadth }\left(b\right)=9\text{ units}\\ \text{Height }\left(h\right)=10\text{ units}\end{array}$

Formula used:

  $\begin{array}{l}\text{Volume of the Prism }\left(V\right)=\frac{1}{2}\times l\times b\times h{\text{ units}}^3\\ \text{Total Surface Area of the Prism }\left(A\right)=\left(b\times b\right)+\left(2\times b\times h\right)+\left(l\times h\right)\end{array}$

Calculation:

Volume of the Prism is,

  $\begin{array}{c}V=\frac{1}{2}\times l\times b\times h\\ =\frac{1}{2}\times 15\times 9\times 10\\ =15\times 9\times 5\\ =675{\left(\text{units}\right)}^3\end{array}$

  

Total surface are of the Prism is

  $\begin{array}{c}A=\left(b\times b\right)+\left(2\times b\times h\right)+\left(l\times h\right)\\ =\left(9\times 9\right)+\left(2\times 9\times 10\right)+\left(10\times 15\right)\\ =81+180+150\\ =411{\text{ units}}^2\end{array}$

  

c

To determine

To calculate : The volume and the total surface are of Cone.

Answer to Problem 3RP

The volume and total surface area of the Cone are, $\left(V\right)=100{\text{π units}}^3$ and $\left(A\right)=90{\text{π units}}^2$

Explanation of Solution

Given information:

  $\begin{array}{l}\text{Slant height }\left(l\right)=13\text{}\text{units}\\ \text{Height }\left(h\right)=12\text{ units}\end{array}$

Formula used:

Radius of the base of the cone is, $r=\sqrt{l^2-h^2}$ units.

Volume of the cone is, $V=\frac{1}{3}\times \pi r^2\times h{\text{ units}}^3$

Total surface area of the cone is, $A=\left(\pi r^2\right)+\left(\pi rs\right){\text{ units}}^2$

Calculation:

Radius of the Cone is, $r=\sqrt{s^2-h^2}=\sqrt{{13}^2-{12}^2}=\sqrt{169-144}=\sqrt{25}=5\text{ units}$

Volume of the Cone is, $V=\frac{1}{3}\times \pi r^2\times h=\frac{1}{3}\times 5^2\times 12\times \pi =100\pi {\text{ units}}^3$

Total Surface Area of the Cone is, $A=\left(\pi r^2\right)+\left(\pi rs\right)=\left(5^2\right)\pi +\left(5\times 13\right)\pi =25\pi +65\pi =90\pi {\text{ units}}^2$