Helppp please The object below is made of solid plastic. It is a cylinder with an indentation at the top in the shape of a cone. What is the volume, to the nearest tenth of a cubic inch, of the plastic object? Explain your answer.

Total volume = (145/3)π in³

Step-by-step explanation:

First find the volume of the entire cylinder.  The correct formula to use here is:

V = πr²h, where r is the radius and h is the height.  Here, with the radius being 5/2 inches and the height being 8 inches, the cylinder volume is

V = π(2.5 in)²(8 in) = 50π in³

Next find the volume of the conical shape:  V = (1/3)π(2.5 in)²(0.8 in)

The desired volume is equal to the volume of the entire cylinder LESS the volume of the cone:

π(2.5 in)²(8 in) = 50π in³  LESS  (1/3)π(2.5 in)²(0.8 in), which simplifies as follows:

Total volume =

50 π in³ -  (1/3)π(2.5 in)²(0.8 in), or

(2.5 in)²π[8 in - 0.8/3 in] =  π(6.25 in²)(8 in - 8/30 in) = π( 6.25 in²)(116/15 in), or

Total volume = (145/3)π in³

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

question

what is the value of the third quartile of the data set represented by this box plot? a. 19 b. 21 c. 26 d. 29

answer

c