what is the volume of the item described?

a capsule consisting of a cylinder of radius 3 mm and height 6 mm with a hemisphere on each end of radius 3 mm.

select the exact answer in terms of π and the approximate answer rounded to the nearest whole number.

283 mm³

81 π mm³

90 π mm³

254 mm³

54 π mm³

170 mm³

The capsule describe consists of 2 hemispheres (same) and 1 cylinder. We need to sum up the volume of the cylinder and the 2 same hemispheres.

We are given the radius of the cylinder as 3 and the height as 6. The formula for volume of cylinder is . Plugging in 3 for r and 6 for h gives us,

.

We are given the radius is 3 for the hemisphere. The formula for volume of a hemisphere is half of the volume of a sphere. The formula for hemisphere is shown below.

. Plugging in 3 for r gives us,

Now, since we have 2 same hemispheres, we multiply this answer by 2 to get total volume of the 2 hemispheres.

.

In decimal, taking 3.14 as , it is

Rounding to the nearest whole number gives us 283 millimeters squared.

ANSWER: Volume = and

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".