Question

Solve this to pretty pretty pls

Answer 1

Answer:

3) 161

Step-by-step explanation:

Indeed this is pretty easy :D

What we need to find is the surface area of the rectangular prism excluding the area of the hole. First, let's find out the width of the box, we can do this by using the area, the length, and the height, and we can write:

$V=lhw$

(Formula to find the volume of a rectangular prism)

$140=(4)(7)w\\ 140=28w\\ 5=w$

Now that we have the width, can find the area of the top part of the prism:

$(5)(4)=20$

The area of the top part of the prism is 20, and the circle has 1/4 of the area of that:

$A_{circle} = \frac{A_{top part} }{4}\\ A_{circle} = \frac{20}{4} \\ A_{circle} = 5$

So the area of the circle is 5. Now we just need to find the surface area of the rectangular prism and subtract that result with the area of the circle:

$A_{circle}=5\\ SA_{rec.pri.}=2(lh+lw+wh)\\ SA_{rec.pri.}=2((4)(7)+(4)(5)+(5)(7))\\ SA_{rec.pri.}=2(28+20+35)\\ SA_{rec.pri.}=2(83)\\ SA_{rec.pri.}=166$

Subtract these two results...:

$166-5=161$

And we are done!