GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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Example Questions

Example Question #122 : 3 Dimensional Geometry

An office uses cone-shaped paper cups for water in their water cooler. The cups have a radius of  inches and a height of  inches. If the water cooler can hold  cubic inches of water, how many complete cups of water can the water cooler fill?

Possible Answers:

Correct answer:

Explanation:

Start by finding the volume of a cup.

Recall how to find the volume of a cone:

Plug in the given radius and height to find the volume.

Now divide the total volume of the water in the water cooler by the volume of one cup in order to find how many complete cups the water cooler can fill.

Since the question asks for the number of complete cups that can be filled, we must round down to .

Example Question #121 : 3 Dimensional Geometry

How many edges and vertices are found on a square pyramid?

Possible Answers:

Correct answer:

Explanation:

The base of a square pyramid is, as the name suggests, a square which has edges and vertices. The vertices of the square each have edges that meet at a single point, adding an additional vertex and additional edges. Together, a square pyramid has edges and vertices.

Example Question #122 : 3 Dimensional Geometry

How many vertices does an octagonal pyramid have?

Possible Answers:

Seven

Eight

Six

Nine

Correct answer:

Nine

Explanation:

An octagonal pyramid has a base with eight vertices, each of which is a vertex of the pyramid. There is one more vertex, or the apex, which is connected to each of the vertices of the base by an edge. Nine is the correct choice.

Example Question #1 : Faces And Surface Area

A circular swimming pool at an apartment complex has diameter 18 meters and depth 2.5 meters throughout. 

The apartment manager needs to get the interior of the swimming pool painted. The paint she wants to use covers 40 square meters per can. How many cans of paint will she need to purchase?

You may use 3.14 for .

Possible Answers:

Correct answer:

Explanation:

The pool can be seen as a cylinder with depth (or height) 2.5 meters and a base with diameter 18 meters - and radius half this, or 9 meters. 

The bottom of the pool - the base of the cylinder - is a circle with radius 9 meters, so its area is

 square meters.

Its side - the lateral face of the cylinder - has area

 square meters.

Their sum - the total area to be painted - is  square feet. Since one can of paint covers 40 square meters, divide:

Nine cans of paint and part of a tenth will be required, so the correct response is ten.

Example Question #1 : Faces And Surface Area

A water tank takes the shape of a sphere whose exterior has radius 24 feet; the tank is six inches thick throughout. To the nearest hundred, give the surface area of the interior of the tank in square feet.

Use 3.14 for .

Possible Answers:

Correct answer:

Explanation:

Six inches is equal to 0.5 feet, so the radius of the interior of the tank is 

 feet.

The surface area of the interior of the tank can be calculated using the formula

,

which rounds to 6,900 square feet.

Example Question #2 : Faces And Surface Area

Cone_1

Give the total surface area of the above cone to the nearest square meter.

Possible Answers:

Correct answer:

Explanation:

The base is a circle with radius , and its area can be calculated using the area formula for a circle:

 square meters.

To find the lateral area, we need the slant height of the cone. This can be found by way of the Pythagorean Theorem. Treating the height  and the radius  as the legs and slant height  as the hypotenuse, calculate:

 meters.

The formula for the lateral area can be applied now:

Add the base and the lateral area to obtain the total surface area:

.

This rounds to 186 square meters.

Example Question #3 : Faces And Surface Area

A water tank takes the shape of a closed cylinder whose exterior has a height of 40 feet and a base with radius 15 feet; the tank is three inches thick throughout. To the nearest hundred, give the surface area of the interior of the tank in square feet.

Use 3.14 for .

Possible Answers:

Correct answer:

Explanation:

Three inches is equal to 0.25 feet, so the height of the interior of the tank is 

 feet.

The radius of the interior of the tank is 

 feet.

The surface area of the interior of the tank can be determined by using this formula:

,

which rounds to 5,000 square feet.

Example Question #5 : Faces And Surface Area

Cone_1

Above is a diagram of a conic tank that holds a city's water supply. 

The city wishes to completely repaint the exterior of the tank - sides and base. The paint it wants to use covers 40 square meters per gallon. Also, to save money, the city buys the paint in multiples of 25 gallons. 

How many gallons will the city purchase in order to paint the tower?

Possible Answers:

Correct answer:

Explanation:

The surface area of a cone with radius  and slant height  is calculated using the formula .

Substitute 35 for  and 100 for  to find the surface area in square meters:

 square meters.

The paint covers 40 square meters per gallon, so the city needs

 gallons of paint. 

Since the city buys the paint in multiples of 25 gallons, it will need to buy the next-highest multiple of 25, or 375 gallons.

Example Question #4 : Faces And Surface Area

A regular octahedron has eight congruent faces, each of which is an equilateral triangle. 

A given octahedron has edges of length three inches. Give the total surface area of the octahedron.

Possible Answers:

Correct answer:

Explanation:

The area of an equilateral triangle is given by the formula

.

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is 

.

Substitute :

 square inches.

Example Question #1645 : Ged Math

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle. 

A given regular icosahedron has edges of length two inches. Give the total surface area of the icosahedron.

Possible Answers:

Correct answer:

Explanation:

The area of an equilateral triangle is given by the formula

.

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is 

.

Substitute :

  square inches.

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