The main trunk of a tree is in the shape of a cylinder.The distance around its of the cross section is 47.1cm and its height is 0.7m .
a) What is the radius of the cross section?
b) The volume of wood is there in the trunk? Show your work
a) To find the radius, we need to use the formula for the circumference of a circle:
C = 2πr
where C is the distance around the cross section and r is the radius.
Plugging in the given value:
47.1 = 2πr
Solving for r:
r = 47.1/2π
r ≈ 7.5 cm
Therefore, the radius of the cross section is approximately 7.5 cm.
b) To find the volume of the trunk, we can use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Plugging in the values we found:
V = π(7.5)^2(0.7)
V ≈ 197.4 cm^3
Therefore, there are approximately 197.4 cm^3 of wood in the trunk.