Rubber balls are packaged in a box with dimensions 8.5 cm, 5 cm, 5 cm. Each ball has a diameter of 3 cm. If there are a dozen balls in the box, how
much space in the box is not occupied by the rubber balls? Round your
answer to the nearest tenth.

42.9 cm^3

Step-by-step explanation:

Volume of the box= (base x width x height) = 8.5 x 5 x 5 = 212.5 cm^3

Radius of a ball = 1.5 cm

Volume of a ball = 4/3 * radius^3 * pi = 4/3 x 1.5^3 x pi = 14,137167 cm^3

Volume of the balls = 14,137167 x 12 = 169,646003 cm^3

Final answer = 212.5 - 169,646003 = 42.9 cm^3

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

6.25 grams

step-by-step explanation: