Question

The sun delivers ${10}^3{\mathrm{Wm}}^{-2}$ of electromagnetic flux on the earth's surface. The total power that is incident on a roof of dimensions $6\mathrm{m}\times 30\mathrm{m}$, is

• A. $1.8\times {10}^5\mathrm{W}$
• B. $7.2\times {10}^5\mathrm{W}$
• C. $0.9\times {10}^5\mathrm{W}$
• D. $4.5\times {10}^5\mathrm{W}$

Answer 1

The correct option is A

$1.8\times {10}^5\mathrm{W}$

Step 1: Given Data:

Electromagnetic flux, $I={10}^3{\mathrm{Wm}}^{-2}$

Area of the roof, $A=6\mathrm{m}\times 30\mathrm{m}=180{\mathrm{m}}^2$

Step 2: Formula Used:

The power transmitted per unit area, measured on a plane perpendicular to the direction of the energy's transmission, is known as the intensity or flux of radiant energy.

$P=I\times A\dots \dots \dots \dots \dots \left(1\right)$

Where $P=$Power, $I=$Intensity, $A=$Area

Step 3: Calculation of total power that is incident on a roof:

The total power that is incident on a roof of dimensions $6\mathrm{m}\times 30\mathrm{m}$

First, find the area of a roof, $A=6\mathrm{m}\times 30\mathrm{m}=180{\mathrm{m}}^2$

Substituting the known values in the above formula in equation (1)-

$\begin{array}{rcl}P& =& I\times A\\ & =& {10}^3\times 180\\ & =& 180\times {10}^3\\ & =& 1.8\times {10}^5\mathrm{W}\end{array}$

Hence, option A is the correct answer.