The area of the regular pentagonal base of this prism is 43.06 square units. What is the volume of this prism?
1 answer:
The Volume of this prism is 148.35 cu.units, Option D is the right answer.
<h3>What is Volume ?</h3>The space occupied by a three dimensional object is called Volume.
Area of the base of the prism is the area of the pentagon
Area of the pentagon is given by
The area is given as 43.06 sq. units
On solving the side of pentagon is 5 units
The volume of the pentagonal prism is given by
V = (5/2)abh
where a is the length of apothem , b is the base length and h is the height
V = (5/2) * 3.44 * 5* 3.45
V = 148.35 cu.units
Therefore the Volume of this prism is 148.35 cu.units , Option D is the right answer.
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Draw a diagram to illustrate the problem as shown below.
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
When the smaller gear rotates through a revolution, it sweeps an arc length of
2π(4) = 8π inches.
Part 1
The same arc length is swept by the larger gear. The central angle of the larger gear, x, is
7x = 8π
x = (8π)/7 radians = (8π)/7 * (180/π) = 205.7°
Answer: 205.7° (nearest tenth)
Part 2
When the larger gear makes one rotation, it sweeps an arc length of
2π(7) = 14π inches.
If the central angle for the smaller gear is y radians, then
4y = 14π
y = 3.5π radians = (3.5π)/2π revolutions = 1.75 revolutions
Answer:
The smaller gear makes 1.75 rotations
Answer:
x=-3,y=-2
Step-by-step explanation:
Given 2 expressions
S1:
S2:
Write one equation in terms of any variable (x or y)
Here I am writing S1 in terms of y
Substitute this value of y as the value of y in S2
⇒
Therefore
Substitute this value of x in any of the expressions S1 or S2
Here i am substituting in S2
⇒
Therefore x=-3 and y=-2