Question

A carpenter is making a wooden window frame that has a width of 1 inch.

How much wood does the carpenter need to build the frame?

5.5 + 106 square inches
5.5 + 116 square inches
5.5 + 153 square inches
5.5 + 162 square inches

Answer 1

Answer: A

Step-by-step explanation:

Answer 2

We have been given diagram of a wooden window. We are asked to find the amount of wood that carpenter needs to build the frame.

The amount of wood needed for the window frame will be equal to area of window frame.

We can see that upper part of window is semicircle. The area of the semicircle is half the area of the circle.

$\text{Area of upper part of frame}=\frac{\pi (R^2-r^2)}{2}$, where,

R = Outer radius,

r = Inner radius.

$\text{Area of upper part of frame}=\frac{\pi (6^2-5^2)}{2}$

$\text{Area of upper part of frame}=\frac{\pi (36-25)}{2}$

$\text{Area of upper part of frame}=\frac{11\pi }{2}$

$\text{Area of upper part of frame}=5.5\pi$

The area of lower part of frame will be area of 3 rectangles. 2 same rectangles with length 48 inches and width 1 inch. One rectangle with length 10 inches (12-2) and width 1 inch.

$\text{Area of lower part of window frame}=2\times 48\times 1+10\times 1$

$\text{Area of lower part of window frame}=96+10$

$\text{Area of lower part of window frame}=106$

$\text{Amount of wood needed for frame}=(5.5\pi+106)\text{ in}^2$

Therefore, option A is the correct choice.