Answer:
15
Step-by-step explanation:
Angle 2 is 2x+10
angle 4 is 4x+80
and from the figure we can understand that when we add these 2 equations
We get
6x+ 90= 180
6x = 180 - 90= 90
6x= 90
x = 90 ÷ 6 = 15
answer = 15
We assume the composite figure is a cone of radius 10 inches and slant height 15 inches set atop a hemisphere of radius 10 inches.
The formula for the volume of a cone makes use of the height of the apex above the base, so we need to use the Pythagorean theorem to find that.
h = √((15 in)² - (10 in)²) = √115 in
The volume of the conical part of the figure is then
V = (1/3)Bh = (1/3)(π×(10 in)²×(√115 in) = (100π√115)/3 in³ ≈ 1122.994 in³
The volume of the hemispherical part of the figure is given by
V = (2/3)π×r³ = (2/3)π×(10 in)³ = 2000π/3 in³ ≈ 2094.395 in³
Then the total volume of the figure is
V = (volume of conical part) + (volume of hemispherical part)
V = (100π√115)/3 in³ + 2000π/3 in³
V = (100π/3)(20 + √115) in³
V ≈ 3217.39 in³
Answer:
5.38 inches
Step-by-step explanation:
The formula for Area of an Heptagon
= A=7/4a²cot(180°/7)
Area = 105in²
Side a = ?
The formula for Side a
= √4A ×tan (180°/7)/7
= √4 × 105 × tan (180°/7) /7
= 5.37536 inches
Approximately = 5.38 inches.
Answer:
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Step-by-step explanation:
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