Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values.
Step One
Find the volume of the sphere.
<em>Givens</em>
r = 6 cm
<em>Formula</em>
V = (4/3) pi r^3
<em>Sub and Solve</em>
V = 4/3 pi * 6^3
V = 288 * pi
Step two
Find the radius of the cylinder
<em>Givens</em>
V = 288* pi cm^3
h = 4.5 cm
<em>Formula</em>
V = pi r^h
<em>Sub and solve</em>
288 pi cm^3 = pi r^2 * 4.5 Divide both sides by pi
288 cm^3 = 4.5 r^2 Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2 Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer
Answer:
303.63 sq inches
Step-by-step explanation:
We need to find the area of the two rectangles he cuts and add them together.
The area of a rectangle is given as:
A = L * B
The first rectangle is 16 inches × 12 1/4 inches. Its area is:
A = 16 * 12 1/4 = 16 * 49/4 = 196 sq inches
The second rectangle is 10 1/2 inches by 10 1/4 inches. Its area is:
A = 10 1/2 * 10 1/4 = 21/2 * 41/4 = 107.63 sq inches
The total square inches of construction paper that he needs is:
196 + 107.63 = 303.63 sq inches
There are 33/20 or 1.65 pounds left.
Given:
4 3/4 pounds of clay
1 1/10 pounds of clay for a cup
2 pounds of clay for a jar
Convert the mixed fraction into fractions.
4 3/4 = (4*4+3)/4 = 19/4
1 1/10 = (1*10+1)/10 = 11/10
2 = 2/1
19/4 - 11/10 = (19/4 *5/5) - (11/10 * 2/2) = 95/20 - 22/20
= (95-22)/20 = 73/20 or 3.65 pounds after making a cup
73/20 - 2/1 = 73/20 - (2/1 * 20/20) = 73/20 - 40/20 = 73 - 40 / 20 = 33/20 OR 1.65 pounds left after making a jar.
We can also convert the fractions into decimal numbers.
19/4 = 4.75
11/10 = 1.10
2/1 = 2.00
4.75 - 1.1 - 2 = 1.65 pounds left.
1/2 is simplest form.
Both 13 and 26 are factors of 13.
13 times 1 is 13 and 13 times 2 is 26.
So 13/26 = 1/2.
