1)volume of a ctlinder: 198mm
Radius base: ??
Height of cylinder: 7mm
2)Volume of a triangular prism:60 cu yd
Length of base: ??
Height of base: 6m
Height of prism: 2m
volume of cylinder = πr^2 h
198 = π r^2 (7)
r^2 = 198/(7π) = 9.0036..
appr 9 mm
#2,
I would have to know what kind of a triangle the base is
To find the radius of the base in the first question, we can use the formula for the volume of a cylinder, which is given by V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.
Given that the volume of the cylinder is 198 mm^3 and the height is 7 mm, we can rearrange the formula to solve for the radius.
1) V = πr^2h
198 = πr^2 * 7
To solve for r, divide both sides of the equation by π * 7:
198 ÷ (π * 7) = r^2
To find the square root of both sides to isolate r, calculate:
√(198 ÷ (π * 7)) = r
This will give you the radius of the base of the cylinder.
For the second question, to find the length of the base of a triangular prism, we can use the formula for the volume of a triangular prism, which is given by V = (1/2) * b * h * H, where V is the volume, b is the length of the base, h is the height of the base, and H is the height of the prism.
Given that the volume is 60 cubic yards, the height of the base is 6 meters, and the height of the prism is 2 meters, we can solve for the length of the base.
2) V = (1/2) * b * h * H
60 = (1/2) * b * 6 * 2
To solve for b, divide both sides of the equation by (1/2) * 6 * 2:
60 ÷ ((1/2) * 6 * 2) = b
Simplifying:
60 ÷ 6 = b
Finally, calculate:
10 = b
This will give you the length of the base of the triangular prism.