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Common Core: 7th Grade Math : Grade 7

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

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All Common Core: 7th Grade Math Resources

7 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : 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 cube is sliced vertically?

Possible Answers:

Rectangle

Square

Triangle

Right triangle

Correct answer:

Square

Explanation:

A vertical cut is an up and down cut.

Screen shot 2016 02 26 at 10.47.35 am

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

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Example Question #6 : 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 right rectangular pyramid is sliced vertically?

Possible Answers:

Triangle

Trapezoid

Rectangle

Square

Correct answer:

Triangle

Explanation:

A vertical cut is an up and down cut.

Screen shot 2016 02 26 at 10.47.39 am

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

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Example Question #3 : 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 10.28.17 am

Possible Answers:

Cube

Rectangle

Right Triangle

Triangle

Correct answer:

Rectangle

Explanation:

A horizontal cut is a side to 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.

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Example Question #4 : 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 10.29.37 am

Possible Answers:

Square

Trapezoid

Rectangle

Triangle

Correct answer:

Square

Explanation:

A horizontal cut is a side to 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.

Report an Error

Example Question #3 : 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

Trapezoid

Rectangle

Right triangle

Correct answer:

Rectangle

Explanation:

A horizontal cut is a side to 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.

Report an Error

Example Question #10 : 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:

Right triangle

Trapezoid

Triangle

Rectangle

Correct answer:

Rectangle

Explanation:

A horizontal cut is a side to 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.

Report an Error

Example Question #651 : Grade 7

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

Possible Answers:

Triangle

Rectangle

Trapezoid

Right triangle

Correct answer:

Rectangle

Explanation:

A horizontal cut is a side to 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.

Report an Error

Example Question #652 : Grade 7

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

Possible Answers:

Square

Right triangle

Triangle

Rectangle

Correct answer:

Square

Explanation:

A horizontal cut is a side to 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.

Report an Error

Example Question #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 25t^2 $\displaystyle 25t^2$. Give the circumference of the circle in terms of $\displaystyle t$.

Let $\pi=3.14$ $\displaystyle \pi=3.14$.

Possible Answers:

15t $\displaystyle 15t$

20t^2 $\displaystyle 20t^2$

17.71t $\displaystyle 17.71t$

20t $\displaystyle 20t$

$\displaystyle 17.71 t^2$

Correct answer:

17.71t $\displaystyle 17.71t$

Explanation:

The area of a circle can be calculated as $Area=\pi r^2$ $\displaystyle Area=\pi r^2$, where $\displaystyle r$ is the radius of the circle.

$Area=\pi r^2\Rightarrow 25t^2=\pi r^2\Rightarrow r^2=\frac{25t^2}{\pi}$ $\displaystyle Area=\pi r^2\Rightarrow 25t^2=\pi r^2\Rightarrow r^2=\frac{25t^2}{\pi}$

$\Rightarrow r=\frac{5t}{\sqrt{\pi}}=\frac{5t}{\sqrt{3.14}}\approx 2.82t$ $\displaystyle \Rightarrow r=\frac{5t}{\sqrt{\pi}}=\frac{5t}{\sqrt{3.14}}\approx 2.82t$

The circumference can be calculated as $Circumference =2\pi r$ $\displaystyle Circumference =2\pi r$, where $\displaystyle r$ is the radius of the circle.

$Circumference =2\pi r\Rightarrow Circumference =2\times 3.14\times 2.82t=17.71t$ $\displaystyle Circumference =2\pi r\Rightarrow Circumference =2\times 3.14\times 2.82t=17.71t$

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Example Question #2 : Perimeter

The perimeter of a given rectangle is equal to the circumference of a given circle. The circle has radius $\displaystyle 30$ inches; the width of the rectangle is $8 \pi$ $\displaystyle 8 \pi$ inches. What is the length of the rectangle?

Possible Answers:

$(30 - 8 \pi )$ $\displaystyle (30 - 8 \pi )$ inches

$7\pi$ $\displaystyle 7\pi$ inches

$44 \pi$ $\displaystyle 44 \pi$ inches

$14 \pi$ $\displaystyle 14 \pi$ inches

$22 \pi$ $\displaystyle 22 \pi$ inches

Correct answer:

$22 \pi$ $\displaystyle 22 \pi$ inches

Explanation:

The circumference of a circle with radius $\displaystyle 30$ inches is

$C = 2 \pi r = 2 \pi \cdot 30 = 60 \pi$ $\displaystyle C = 2 \pi r = 2 \pi \cdot 30 = 60 \pi$ inches.

The perimeter of the rectangle is therefore $60 \pi$ $\displaystyle 60 \pi$ inches. To find its length, substitute $W = 8\pi$ $\displaystyle W = 8\pi$ and $P = 60\pi$ $\displaystyle P = 60\pi$ into the equation and solve for $\displaystyle L$:

$\displaystyle 2 L + 2W = P$

$2 L + 2 \cdot 8 \pi = 60 \pi$ $\displaystyle 2 L + 2 \cdot 8 \pi = 60 \pi$

$2 L + 16 \pi = 60 \pi$ $\displaystyle 2 L + 16 \pi = 60 \pi$

$2 L + 16 \pi - 16 \pi = 60 \pi - 16 \pi$ $\displaystyle 2 L + 16 \pi - 16 \pi = 60 \pi - 16 \pi$

$2 L =44 \pi$ $\displaystyle 2 L =44 \pi$

$2 L \div 2=44 \pi \div 2$ $\displaystyle 2 L \div 2=44 \pi \div 2$

$L = 22\pi$ $\displaystyle L = 22\pi$ inches

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All Common Core: 7th Grade Math Resources

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Common Core: 7th Grade Math : Grade 7

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #5 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #6 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #3 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #4 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #3 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #10 : Describe The Two Dimensional Figures That Result From Slicing Three Dimensional Figures: Ccss.Math.Content.7.G.A.3

Example Question #651 : Grade 7

Example Question #652 : Grade 7

Example Question #1 : Know And Use The Formulas For The Area And Circumference Of A Circle: Ccss.Math.Content.7.G.B.4

Example Question #2 : Perimeter

All Common Core: 7th Grade Math Resources

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