The diagram shows a semi circle inside a rectangle of length 140m. the semi circle touches the rectangle at P, Q and R. Calculat
e the perimeter of the shaded region. give your answer correct to 3 significant figures. ITS ON MATHSWATCH PLS HELP!!!
1 answer:
Answer: 250m
Step-by-step explanation:
Length of rectangle = 140m
Length of rectangle = diameter of semicircle = 140m
Therefore, Radius(r) = 140m / 2 = 70m
Perimeter of the shaded region:
Length of tangent at P + length of tangent at Q + shaded portion of arc(AB)
Length of tangent = diameter / 2
Length of tangent = 70m
Perimeter of a circle = 2πr = 2 × 22/7 × 70 = 440m
shaded portion = 440 / 4 = 110m
Therefore, perimeter of shaded portion equals
70m + 70m + 110m = 250m
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Sum of all angles of a triangle is equal to 180°. Therefore,
A + B + C = 180
Given that, A = 4x, B = 3x + 1, C = 7x + 11.
Hence, we can set up an equation as following:
4x + 3x + 1 + 7x + 11 = 180
14x + 12 = 180 Combine the like terms.
14x + 12 -12 = 180 - 12 Subtract 12 from each sides.
14x = 168
Divide each sides by 14.
So, x= 12.
Now by plug in x=12 in the given expressions of A, B and C we can get the measure of eah angles of the triangle. Therefore,
A = 4x = 4(12) = 48
B= 3x + 1= 3(12) + 1 = 36 + 1 = 37
C= 7x + 11 = 7(12) + 11 = 84 + 11 =95
From the above result we can see that C is the largest angle and B is the smallest angle.
There is a relationship of a triangle which state that the largest side is opposite side of the largest angle and similarly smallest side is opposite side of the smallest angle.
Here AB is the opposite side of the largest angle C. So, AB is the largest side.
Similarly AC is the smallest side.
So, the order from shortest to longest is B: AC, BC, AB
Answer:20mm
Step-by-step explanation:
Answer:
The radius of the cylinder is equal to
Step-by-step explanation:
we know that
The volume of a cylinder is equal to
In this problem we have
Substitute in the formula and solve for r