Chapter 11.6, Problem 4P

To determine

Tocheck:whether the table top of the 210 cm diameter is carried through the given door-way.

Answer to Problem 4P

Yes, it is easy to carried through the given door-way.

Explanation of Solution

Given:

The dimensions of the given door-way is $200\text{cm}\times 90\text{cm}$ .

Calculation:

According to the question, the dimensions of the given door-way is $200\text{cm by}90\text{cm}$ .

Therefore, the area of the given door-way is $A=200\text{cm}\times 90\text{cm}=18000{\text{cm}}^2$ .

Now, to find the area of the table top whose diameter is 210cm. Thus,

Radius of the table top is $r=\frac{210}{2}=105\text{cm}$ . Therefore,

Area of the table top is:

  $\begin{array}{l}A=\pi r^2\\ A=\frac{22}{7}{\left(105\right)}^2\left\{\text{substitutes }\pi =\frac{22}{7}\text{ and}r=105\right\}\\ A=\frac{22}{7}\left(105\right)\left(105\right)\\ A=22\times \left(15\right)\left(105\right)\\ A=34650c{m}^2\end{array}$

Thus, the area of the table top is $A=34650{\text{cm}}^2$ and the area of the doorway is $A=18000{\text{cm}}^2$ .

Since, the area of the door-way is greater than the area of the table top.

Therefore, it is easy to carriedthe table top through the given door-way.