Answer:
96 m²
Step-by-step explanation:
The unshaded region is a right triangle.
The area (A) of the triangle is calculated as
A = bh ( b is the base and h the perpendicular height )
Calculate b using Pythagoras' identity in the right triangle
b² + 16² = 20²
b² + 256 = 400 ( subtract 256 from both sides )
b² = 144 ( take the square root of both sides )
b = = 12
Thus area of unshaded region is
A = × 12 × 16 = 6 × 16 = 96 m²
Answer:
The first thing we need to do is to find the area bounded by:
y = x^3
y = 0
between:
x = 0 and x = 2
This is the integral of the given function between x = 0 and x = 2, written as:
This means that the area of the bounded region is 4 square units.
Now, if we do a full rotation around the x-axis, the volume generated will be equal to the area that we obtained times 2*pi units.
The volume is:
V = (4 square units)*(2*pi units) = 8*pi cubic units.
(Notice that no option coincides with this, there may be a mistake in the options)