All HiSET: Math Resources
Example Questions
Example Question #1 : Area
Find the area of a square with the following side length:
We can find the area of a circle using the following formula:
In this equation the variable, , represents the length of a single side.
Substitute and solve.
Example Question #21 : Properties Of Polygons And Circles
The perimeter of a square is . In terms of
, give the area of the square.
Since a square comprises four segments of the same length, the length of one side is equal to one fourth of the perimeter of the square, which is . The area of the square is equal to the square of this sidelength, or
.
Example Question #1 : Area
The volume of a sphere is equal to . Give the surface area of the sphere.
None of the other choices gives the correct response.
The volume of a sphere can be calculated using the formula
Solving for :
Set . Multiply both sides by
:
Divide by :
Take the cube root of both sides:
Now substitute for in the surface area formula:
,
the correct response.
Example Question #1 : Area
Express the area of a square plot of land 60 feet in sidelength in square yards.
600 square yards
3,600 square yards
600 square yards
400 square yards
200 square yards
400 square yards
One yard is equal to three feet, so convert 60 feet to yards by dividing by conversion factor 3:
Square this sidelength to get the area of the plot:
,
the correct response.
Example Question #1 : Area
A square has perimeter . Give its area in terms of
.
Divide the perimeter to get the length of one side of the square.
Divide each term by 4:
Square this sidelength to get the area of the square. The binomial can be squared by using the square of a binomial pattern:
Example Question #91 : Hi Set: High School Equivalency Test: Math
A cube has surface area 6. Give the surface area of the sphere that is inscribed inside it.
A cube with surface area 6 has six faces,each with area 1. As a result, each edge of the cube has length the square root of this, which is 1.
This is the diameter of the sphere inscribed in the cube, so the radius of the sphere is half this, or . Substitute this for
in the formula for the surface area of a sphere:
,
the correct choice.
All HiSET: Math Resources
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