Right triangle ABC, shown, has a vertical leg 6 inches long and a hypotenuse 10 inches long. If the triangle was rotated 360 degrees around the vertical leg to form a right circular cone, what would be the volume of this cone, in cubic inches?
A. 32
B. 96
C. 128
D. 288
E. 384

The answer to your question is the letter D. 288 in³

Step-by-step explanation:

Data

Radius = 6 in

height = ?

g = 10 in

Volume = ?

Formula

Volume of a cone = πr²h / 3

Process

1.- Find height using the Pythagorean theorem

            height² = 10² - 6²

                         = 100 - 36

                         = 64

            height = 8

2.- Find the volume of the cone

            Volume = π(6)²(8)

Simplification

            Volume = π(36)(8)

Result

             Volume = 288π in³

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.