ISEE Middle Level Math : Geometry
Study concepts, example questions & explanations for ISEE Middle Level Math
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Example Questions
Example Question #1 : Solid Geometry
Give the volume of the above box in cubic centimeters.
100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.
Use the volume formula, substituting 
Example Question #2 : Solid Geometry
A cube made of nickel has sidelength 20 centimeters, Nickel has a density of 8.9 grams per cubic centimeter. What is the mass of this cube?
The volume of the cube is 
Example Question #1 : Volume Of A Rectangular Solid
A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its volume in cubic feet.
Divide each dimension in inches by 12 to convert from inches to feet:
Multiply the three to get the volume:
Example Question #3 : Solid Geometry
Give the volume of the box in cubic inches.
Use the volume formula, substituting 
Example Question #3 : How To Find The Volume Of A Net
One cubic foot is equal to (about) 7.5 gallons.
The above depicts a rectangular swimming pool for an apartment. The pool is seven feet deep everywhere. How many gallons of water does the pool hold?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 7 feet; its volume in cubic feet the product of these dimensions, which is
One cubic foot is equal to about 7.5 gallons, so multiply:
Example Question #4 : How To Find The Volume Of A Net
The above depicts a rectangular swimming pool for an apartment. The pool is six feet deep everywhere. What is the volume of the pool in cubic feet?
The pool can be seen as a rectangular prism with dimensions 50 feet by 35 feet by 6 feet; its volume is
Example Question #1 : How To Find The Perimeter Of Square
Use this image for the following problem.
What is the perimeter of the square in this picture?
The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles.
Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.
Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take 
Our perimeter is 
Example Question #1 : Quadrilaterals
Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up 
When Sandy puts the border around her son's room, she will need enough to cover the perimeter. Since the room has four walls equal in length, we know that the room is a square. The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4. This can be written as:
Since we know that Sandy used 
Now, in order to isolate the variable, we can divide both sides by four.
The left-hand side simplifies to:
The right-hand side simplifies to:
When we solve, we find that the length of each wall is 
Example Question #2 : Quadrilaterals
Find the perimenter:
The perimeter is equal to the sum of the length of all sides. Each side is equal to 
Example Question #3 : Quadrilaterals
Find the perimeter of a square with side length 10.
To solve, simply multiply the side length by 4 since all sides in a square area equal. Thus,
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