The volume V of a pyramid is given by the formula V=1/3Bh, where B is the area of the base and h is the height.
2 answers:
Answer:
a)
b) The height of the pyramid is 18 cm.
Step-by-step explanation:
Given : The volume V of a pyramid is given by the formula , where B is the area of the base and h is the height.
To find :
a. Solve the formula for h
b. Find the height of the pyramid
Solution :
We have given the Volume of the pyramid is V=216 cubic cm.
The base of the pyramid is B=36 square cm.
a) The formula of volume of pyramid is
b) Substitute the values in the formula,
Therefore, The height of the pyramid is 18 cm.
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The triangle is missing, so i have attached it.
Answer:
1)sin(α) = 4/7
2)cos(β) = 4/7
3)tan(α) = 4/√33
4)cot(β) = 4/√33
5)sec(α) = 7/√33
6)csc(β) = 7/√33
Step-by-step explanation:
(1) sin(α)
From trigonometric ratios, we know that sine of an angle in a right angle triangle = opposite/hypotenuse.
Now, in this question, the opposite side to α is 4 and the hypotenuse is 7. Thus, sin(α) = 4/7
2) cos(β)
Cosine of an angle = adjacent side/hypotenuse.
In the question, the adjacent side to the angle β is 4 and the hypotenuse is 7. Thus, cos(β) = 4/7
3)tan(α)
tan of an angle = opposite/adjacent side. The opposite side to α is 4, but the adjacent side is unknown.
Using the pythagoras theorem,
Adjacent side = √(7² - 4²)
Adjacent side = √(49 - 16)
Adjacent side = √33.
Thus, tan(α) = 4/√33
4) cot(β)
cot of an angle is the reciprocal of tangent of same angle.
The adjacent side to β is 4 while the opposite is √33.
So, tan(β) = (√33)/4
cot(β) = 1/tan(β)
cot(β) = 1/[(√33)/4]
cot(β) = 4/√33
5)sec(α)
sec of an angle is equal to one divided by cosine of that same angle, so it equals hypotenuse divided by the adjacent. The hypotenuse is 7 and the adjacent side to α is √33.
Thus, sec(α) = 1/cosα = 7/√33.
6) csc(β)
Csc of an angle is equal to one divided by sine of same angle, so it equals hypotenuses divided by the opposite. The hypotenuse is 7 and the opposite side to β is √33.
Thus, csc(β) = 1/sin(β) = 7/√33
