Answer:
85 nails
Step-by-step explanation:
First, we need to calculate the volume of a single nail. It consists of a circular cylinder and hemispherical part.
The volume of the cylinder πr^2 • h. We are given the diameter of the cylinder (14 mm), so radius is half of that (r = 7 mm) and we are given the height (h = 20 mm).
So, the volume of the cylinder is:
V1 = π • 7^2 • 20
V1 = 3077.2 mm^3
Now for the volume of the hemisphere part. Its volume is half of the sphere:
V2 = (4/3 • πr^3) / 2
Diameter of the sphere is given and it is 21 mm, so the radius is 10.5 mm. So, the volume is:
V2 = (4/3 • π • 10.5^3) / 2
V2 = 2423.3 mm^3
So, the volume of the nail is V1 + V2 which is 5500.5 mm^3
Now let's convert volume of the metal used for making nails. It's given that it is 550.55 cm^3 which is 550550 mm^3.
It is also said that 15% of the volume is wasted, so we are left with 85% of the volume, which is 550550 • 0.85 and that equals to 467967.5 mm^3. So to find a number of nails made from this volume, we divide:
467967.5 / 5500.5 = 85 nails
Answer and Step-by-step explanation:
what must be true is that this particular two lines are not a set of PARALLEL lines. When the lines are parallel, the corresponding angles are congruent and the then the pairs of consecutive angles formed are supplementary .
If we are takling about corresponding angles, they will not be congruent if the lines are not parallel
Answer:
x = 2.5
Step-by-step explanation:
The arc length x is calculated as
x = circumference of circle × fraction of circle
= 2πr × 
( cancel 2π on numerator/ denominator )
x = 1 × 2.5 = 2.5
To answer this you will use the formula for finding area of a parallelogram.
A = bh
3 inches x 2 inches
A = 6 square inches per piece of paper
6 square inches x 15 = 90 square inches
90 in.² of paper is used to make 15 pieces.
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