Consider the point where the hexagons meet the positive half of the y axis.
The inner hexagon meets the axis at 
, whereas the outer hexagon meets the axis at 
So, we're looking for a dilation constant 
such that
So, solving by k we have
We know that the side lengths of the square base are: x * x. The volume is 12, so for now, let's say that y is the other side length. Then, x * x * y = 12. We can solve for y: y = 12/x^2. Now, we find the surface area of the 5 sides.
Four of the sides have the same area: x * (12/x^2) = 12/x, so we multiply this by 4: 48/x.
The last side is the base: x * x = x^2.
We add 48/x to x^2:
x^2 + 48/x
So, the answer is the fourth choice, (d).
Answer:Area of the shaded region is 73.6 cm^2
Step-by-step explanation:
The circle is divided into two sectors. The Smaller sector contains the triangle. The angle that the smaller sector subtends at the center of the circle is 80 degrees. Since the total angle at the center of the circle is 360 degrees, it means that the angle that the larger sector subtends at the center would be 360 - 80 = 280 degrees
Area of a sector is expressed as
Area of sector = #/360 × πr^2
# = 280
r = 5 cm
Area of sector = 280/360 × 3.14 × 5^2
Area of sector = 61.06 cm^2
Area of the triangle is expressed as
1/2bh = 1/2 × 5 × 5 = 12.5
Area of the shaded region = 61.06 +
12.5 = 73.6
