Answer:
The total area that is painted yellow is
Step-by-step explanation:
we know that
The area of the outside of the box is equal to the surface area of the box minus the area of the top
The area of the outside is
where
B is the area of the base
P is the perimeter of the base
H is the height of the box
<em>Find the area of the base B</em>
<em>Find the perimeter of the base P</em>
we have
substitute the values
Answer:
see below for a graph
Step-by-step explanation:
Completing the square for x and y terms can help you put this in the standard form.
(x^2 +10x) +(y^2 +6y) = -18
(x^2 +10x +25) +(y^2 +6x +9) = -18 +25 +9 . . . . add square of half linear coefficient
(x +5)^2 +(y +3)^2 = 16 . . . . . . . circle centered at (-5, -3) with radius 4
Answer:
Part A)
The lower base has a radius of 9 units, and the upper base has a radius of 6 units.
Part B)
5 units.
Part C)
75π or about 235.62 square units.
Step-by-step explanation:
Please refer to the figure below.
The cone has a radius of 9 units and a total height of 12 units.
A frustum of the cone has a height of 4 units.
Part A)
The lower radius of the frustum will simply be 9 units.
For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:
Solve for <em>x.</em> Simplify:
Cross-multiply:
The upper base has a radius of 6 units.
Part B)
We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:
Simplify:
Now, find the slant height of the upper cone:
So:
Then the slant height of the frustum will be the cone subtracted from the total. Thus:
Part C)
We can first find the lateral area of the entire cone. The lateral area is given by:
The lateral area of the entire cone will be:
The lateral area of the upper cone will be:
Then the lateral area of the frustum is:
