2/13_
Step-by-step explanation:
6/39_=
_6÷39/3
=2/39_
=11÷2/39_
=2/13_
We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ =

π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.
R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14
a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = <span>π r² h
</span><span>V₁ = </span>3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³
b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × <span>V₂
</span>Vₐ = 3 × <span>

π r³
</span>Vₐ = 3 ×

3.14<span> (6.5 cm)³</span>
Vₐ = 3,449.3 cm³
c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V =

×100
V =

×100
V = 0.6666 ×100
V = 66.66%
Answer:
8 by 12 units
Step-by-step explanation:
Let w represent the width of the rectangle. Then the length is 1.5w. The perimeter is 4 more than 3 times this, so is (3(1.5w) +4) = 4.5w+4
The perimeter is given by the formula ...
P = 2(length + width)
Filling in the given values for the variables, we have ...
4.5w +4 = 2(w +1.5w)
4 = 0.5w . . . . . . subtract 4.5w and collect terms
8 = w . . . . . . . . . multiply by 2
length = 1.5×8 = 12
The rectangle is 8 units wide and 12 units long. The perimeter is 40 units.