"a solid machine part is to be manufactured as shown in the figure. the part is made by cutting a small cone off the top of a larger cone. the small cone has a base radius of 3 inches and a height of 5 inches. the larger cone has a base radius of 5 inches and had a height of 12 inches prior to being cut. what is the volume of the resulting part illustrated in the figure? "

i keep doing the math for it and get 359 cubed inches (rounded to the closest whole number) when including the pi, and 114*pi cubed inches when i exclude it. the answer choices are 60*pi cubed inches, 65*pi cubed inches, 85*pi cubed inches, and 90*pi cubed inches. can someone go through the math of this?

Large cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Smaller cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches 

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form