A cone is cut into a cube as shown below. If the cone has a diameter of 9 inches with a slant height of 7.5 inches, find the total surface area of the solid.

169.67in²

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The expression for the total surface area of the cone is

A= πrl + πr²

Given data

Diameter d =9in

Radius r = d/2= 9/2= 4.5in

Slant height l = 7.5in

A= πrl + πr²

Substituting our given data we have

A= 3.142*4.5*7.5+ 3.142*4.5²

A= 106.04+63.63

A= 169.67in²

The total surface area is 169.67in²

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.