All Common Core: 7th Grade Math Resources
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?
Triangle
Rectangle
Right triangle
Trapezoid
Rectangle
水平降低的一面side cut.
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?
Triangle
Right triangle
Rectangle
Trapezoid
Rectangle
水平降低的一面side cut.
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?
Trapezoid
Triangle
Right triangle
Rectangle
Rectangle
水平降低的一面side cut.
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?
Rectangle
Triangle
Square
Right triangle
Square
水平降低的一面side cut.
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.
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?
inches
inches
inches
inches
inches
inches
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.?
7744 – 1936π dollars
1936 – 484π dollars
5808 dollars
1936π dollars
1936 dollars
1936 – 484π dollars
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.?
500 - 125π dollars
2500 - 625π dollars
500 dollars
625 - 25π dollars
625 dollars
500 - 125π dollars
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?
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?
Not enough information is given to answer this question.
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