Common Core: 7th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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例子问题tions

例子问题tion #1 :Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

What is the two dimensional shape that is created when the shape provided is sliced horizontally?

Screen shot 2016 02 26 at 10.41.26 am

Possible Answers:

Triangle

Rectangle

Right triangle

Trapezoid

Correct answer:

Rectangle

Explanation:

水平降低的一面side cut.

Screen shot 2016 02 26 at 10.59.43 am

This shape is a right rectangular pyramid, which has a base of a rectangle and sides in the shape of triangles; thus, a horizontal cut would make a rectangle.

例子问题tion #1 :Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

What is the two dimensional shape that is created when a rectangular prism is sliced horizontally?

Possible Answers:

Triangle

Right triangle

Rectangle

Trapezoid

Correct answer:

Rectangle

Explanation:

水平降低的一面side cut.

Screen shot 2016 02 26 at 10.59.58 am

This shape is rectangular prism, which has a base and sides in the shape of rectangles; thus, the two dimensional shape is a rectangle.

例子问题tion #651 :Grade 7

What is the two dimensional shape that is created when a right rectangular pyramid is sliced horizontally?

Possible Answers:

Trapezoid

Triangle

Right triangle

Rectangle

Correct answer:

Rectangle

Explanation:

水平降低的一面side cut.

Screen shot 2016 02 26 at 10.59.43 am

This shape is a right rectangular pyramid, which has a base of a rectangle and sides in the shape of triangles; thus, a horizontal cut would make a rectangle.

例子问题tion #652 :Grade 7

What is the two dimensional shape that is created when a cube is sliced horizontally?

Possible Answers:

Rectangle

Triangle

Square

Right triangle

Correct answer:

Square

Explanation:

水平降低的一面side cut.

Screen shot 2016 02 26 at 11.00.04 am

This shape is cube, which has a base and sides in the shape of squares; thus, the two dimensional shape is a square.

例子问题tion #1 :Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

The area of a circle is. Give the circumference of the circle in terms of.

Let.

Possible Answers:

Correct answer:

Explanation:

The area of a circle can be calculated as, whereis the radius of the circle.

The circumference can be calculated as, whereis the radius of the circle.

例子问题tion #1 :How To Find Circumference

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radiusinches; the width of the rectangle isinches. What is the length of the rectangle?

Possible Answers:

inches

inches

inches

inches

inches

Correct answer:

inches

Explanation:

The circumference of a circle with radiusinches is

inches.

The perimeter of the rectangle is thereforeinches. To find its length, substituteandinto the equation and solve for:

inches

例子问题tion #23 :Radius

A manufacturer makes wooden circles out of square blocks of wood. If the wood costs $0.25 per square inch, what is the minimum waste cost possible for cutting a circle with a radius of 44 in.?

Possible Answers:

7744 – 1936π dollars

1936 – 484π dollars

5808 dollars

1936π dollars

1936 dollars

Correct answer:

1936 – 484π dollars

Explanation:

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 88 inches for our problem. Its total area would be 88 * 88 or 7744 in2.

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle isπr2orπ * 442= 1936π in2. Therefore, the area remaining would be 7744 – 1936π. The cost of the waste would be 0.25 * (7744 – 1936π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 4 from our subtraction. This would give us: 0.25 * 4 * (1936 – 484π). Since 0.25 is equal to 1/4, 0.25 * 4 = 1. Therefore, our final answer is: 1936 – 484π dollars.

例子问题tion #12 :How To Find The Area Of A Circle

A manufacturer makes wooden circles out of square blocks of wood. If the wood costs $0.20 per square inch, what is the minimum waste cost possible for cutting a circle with a radius of 25 in.?

Possible Answers:

500 - 125π dollars

2500 - 625π dollars

500 dollars

625 - 25π dollars

625 dollars

Correct answer:

500 - 125π dollars

Explanation:

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 50 inches for our problem. Its total area would be 50 * 50 or 2500 in2.

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2or π * 252= 625π in2. Therefore, the area remaining would be 2500 - 625π. The cost of the waste would be 0.2 * (2500 – 625π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 5 from our subtraction. This would give us: 0.2 * 5 * (500 – 125π). Since 0.2 is equal to 1/5, 0.2 * 625 = 125. Therefore, our final answer is: 500 – 125π dollars.

例子问题tion #2 :Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

What is the circumference of the circle provided?


6

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to recall the formula for the circumference of a circle:

or

The circle in this question provides us with the radius, so we can use the first formula to solve:

Solve:

例子问题tion #3 :Acute / Obtuse Triangles

One angle of an isosceles triangle has measure. What are the measures of the other two angles?

Possible Answers:

Not enough information is given to answer this question.

Correct answer:

Explanation:

An isosceles triangle not only has two sides of equal measure, it has two angles of equal measure. This means one of two things, which we examine separately:

Case 1: It has anotherangle. This is impossible, since a triangle cannot have two obtuse angles.

Case 2: Its other two angles are the ones that are of equal measure. If we letbe their common measure, then, since the sum of the measures of a triangle is,

两个角度测量

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