# Don't get surface area questions

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• October 11th 2012, 06:51 AM
BobThePizzaBoy
Don't get surface area questions
I posted this last night but I have since gotten answers for one of the questions but still do not get two at all. (Headbang)

1. "Find the total surface area of the following figure.
Hint: The surface area formula for the cone includes the base of the cone. Substract this value."
Image:
http://www.omegamath.com/scripts/geometry/Gtest/image924.gif

I do not get this at all. Someone please just respond with clear directions on how I measure the surface area for this particular image. An answer would be appreciated too of course, it would help in figuring out how I do this!

2. "Find the total surface area of the following figure. The back of the figure is a rectangle. Disregard the bottom of the figure."
Image:
http://www.omegamath.com/scripts/geometry/Gtest/image925.gif

This one seems to be the same way, so same deal as #1.

Thank you in advance!
• October 11th 2012, 09:22 AM
MarkFL
Re: Don't get surface area questions
1.) The lateral surface area of a cone is:

$A_1=\pi rl$

where $r$ is the radius and $l$ is the lateral height.

The surface area of a hemisphere is:

$A_2=\frac{2}{3}\pi r^3$

Now add these the get the total area:

$A=A_1+A_2=\pi rl+\frac{2}{3}\pi r^3=\frac{\pi r}{3}\left(3l+2r^2 \right)$

Now use $r=2\text{ cm}$ and $l=5\text{ cm}$ to find the surface area of the given solid.

2.) The back of the figure is a rectangle having a base $b$ of 16 in and a height $h$ of 7 in.

The area of a rectangle is $A_R=bh$

The two sides are trapezoids having big base $B$ of 7 in and little base $b$ of 3 in and height $h$ of 3 in.

The area of a trapezoid is $A_T=\frac{h}{2}(B+b)$

The front is two rectangles. The vertical rectangle has a base of 16 in and a height of 3 in, and the slanted rectangle has a base of 16 in and a height which is the hypotenuse of a right triangle having legs of 3 in and 4 in. Using the Pythagorean theorem, we find this is:

$\sqrt{3^2+4^2}=5$

So, put this all together to find the requested surface area.
• December 13th 2012, 03:00 AM
gasper43
Re: Don't get surface area questions
I am always fond of mathematics and find it really interesting. Some parts of it like trigonometry always troubled me with the formulas. Even integral calculus was really hard to understand. You are maintaining a nice math forum here.for details
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Gasper Millan