A rectangle has an area of 186m2
1 answer:
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Volume of the pyramid is V = (Bh)/3 where B is the base area of the pyramid and h is the height to the pyramid.
B = 2(2) = 4in²
To find h, we need to use the Pythagorean theorem. The height of the pyramid is actually an altitude that drops straight down from the vertex of the pyramid perpendicular to the Base hitting the Base in the center. Therefore, the distance from where the altitude hits the Base and the edge of the Base is equal to 1. We are given the slant height as 5 inches so we can now use the theorem to find the height of the pyramid.
h² + 1² = 5²
h² = 5² - 1²
h² = 25 - 1
h² = 24
Now we can find the Volume:
V= (Bh)/3
![V= \frac{[4(2 \sqrt{6} )]}{3}](https://tex.z-dn.net/?f=V%3D%20%5Cfrac%7B%5B4%282%20%5Csqrt%7B6%7D%20%29%5D%7D%7B3%7D%20)
This is about 6.5 in³ of volume
B = 2(2) = 4in²
To find h, we need to use the Pythagorean theorem. The height of the pyramid is actually an altitude that drops straight down from the vertex of the pyramid perpendicular to the Base hitting the Base in the center. Therefore, the distance from where the altitude hits the Base and the edge of the Base is equal to 1. We are given the slant height as 5 inches so we can now use the theorem to find the height of the pyramid.
h² + 1² = 5²
h² = 5² - 1²
h² = 25 - 1
h² = 24
Now we can find the Volume:
V= (Bh)/3
This is about 6.5 in³ of volume
Answer:
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost=2046.16 cents
Step-by-step explanation:
Given that a rectangular box with a volume of 684 ft³.
The base and the top of the rectangular box is square in shape
Let the length and width of the rectangular box be x.
[since the base is square in shape, length=width]
and the height of the rectangular box be h.
The volume of rectangular box is = Length ×width × height
=(x²h) ft³
(1)
The area of the base and top of rectangular box is = x² ft²
The surface area of the sides= 2(length+width) height
=2(x+x)h
=4xh ft²
The total cost to construct the rectangular box is
=[(x²×20)+(x²×15)+(4xh×1.5)] cents
=(20x²+15x²+6xh) cents
=(25x²+6xh) cents
Total cost= C(x).
C(x) is in cents.
∴C(x)=25x²+6xh
Putting
Differentiating with respect to x
To find minimum cost, we set C'(x)=0
ft.
Putting the value x in equation (1) we get
≈36.23 ft.
The dimensions of the rectangular box is 36.23 ft×36.23 ft×4.345 ft.
Minimum cost C(x)=[25(4.345)²+10(4.345)(36.23)] cents
=2046.16 cents
Answer:
V = 10,240mm^3
Step-by-step explanation:
The volume of pyramid is given by the following formula:
(1)
b: base of the pyramid = (32mm)^2
h: height
Thus, it is necessary to find the value of h, by using the Pitagoras's theorem, one half of the base and the slant height (which forms a rectangle triangle with h):
by replacing in (1) you obtain:
hence, the volume is 10240mm^3