Question

PLS PLS. send me the answer for the first question with an explanation. due tmrw so quick.​

Answer 1

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