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
The reasonable estimate for the length of side DE is 3 units
Find the diagram of the question attached. The given triangle ABC and BDE are similar triangles.
Using the similarity theorem of a triangle, this is expressed as:
AC = DE
Using the pythagoras theorem to get the length of AC:
AB^2 = AC^2 + BC^2
5^2 + AC^2 + 4^2
AC^2 = 25 - 16
AC^2 = 9
AC= 3
Since AC = DE, hence the reasonable estimate for the length of side DE is 3 units
Learn more on similar shapes here: brainly.com/question/14285697
Answer:
Looks like the scale factor is 1/3.
Step-by-step explanation:
<em>(In this dilation, the green image is polygon ABCDE, and the red image is polygon A'B'C'D'E'. The red image is the resulting image after said dilation.)</em>
A scale factor greater than one enlarges an image, and a scale factor between zero and one shrinks an image, so that rules out options 2 (SF = -3) and 3 (SF = 3).
A negative scale factor would end up in an image opposite the center of enlargement, so that eliminates option 4 (SF = -1/3).
So that means that the scale factor is option 1 (SF = 1/3)!
Answer:
D. 1080°
Step-by-step explanation:
Sum=(n-2)x180°
(8-2)x180°
6x180°
1080°
Hope it helps ❤
Answer:
√5 = 2.236.
Hence the value of root 5 up to 3 decimal places is 2.236.