Find the volume of the square pyramid shown. Round to the nearest tenth if necessary.
1 answer:
Formula
The formula for a pyramid is V = 1/3 * B * h
B = s * s of the square bottom
s = 10
B = 10*10
B = 100 square feet.
Height.
The height is not given. You find it using a^2 + b^2 = c^2
a = 1/2 length of the side of the base
b = height
c = 13^2
If you draw a line to the midpoint of the base form the base of the height, you get 5. You have to read that a couple of times. I don't know if you can see this or not.
AC = 10
B is the midpoint of AC that means that BD = 5
BH = 13 Given
We need HD
Use the pythagorean theorem
HD^2 + BD^2 = BH
HD^2 + 5^2 = 13^2
HD^2 + 25 = 169
HD^2 = 169 - 25
HD^2 = 144 Take the sqrt of both sides.
HD = sqrt(144)
HD = 12
Find the Volume
V = 1/3 * B * H
V = 1/3 * 100 * 12
V = 1/3 * 1200
V = 400
Answer
V = 400 square feet <<< answer
The formula for a pyramid is V = 1/3 * B * h
B = s * s of the square bottom
s = 10
B = 10*10
B = 100 square feet.
Height.
The height is not given. You find it using a^2 + b^2 = c^2
a = 1/2 length of the side of the base
b = height
c = 13^2
If you draw a line to the midpoint of the base form the base of the height, you get 5. You have to read that a couple of times. I don't know if you can see this or not.
AC = 10
B is the midpoint of AC that means that BD = 5
BH = 13 Given
We need HD
Use the pythagorean theorem
HD^2 + BD^2 = BH
HD^2 + 5^2 = 13^2
HD^2 + 25 = 169
HD^2 = 169 - 25
HD^2 = 144 Take the sqrt of both sides.
HD = sqrt(144)
HD = 12
Find the Volume
V = 1/3 * B * H
V = 1/3 * 100 * 12
V = 1/3 * 1200
V = 400
Answer
V = 400 square feet <<< answer
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Answer:
Step-by-step explanation:
The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:
--------------------(i)
From the question,
the point is (5, 0, -6)
the plane is x + y + z = 6
Therefore,
a = 5
b = 0
c = -6
m = 1
n = 1
t = 1
r = 6
Substitute these values into equation (i) as follows;
Therefore, the shortest distance from the point to the plane is