Y8 geometri/uttryck

Omkrets och area

100

Find the area for a square with side length 5 cm.

25 cm²

200

What is the perimeter for an isosceles triangle with a base of 6 cm and other sides 10 cm each?

26 cm

300

A clock has a diameter of 28cm.  Find the area and round to the nearest tenth.

615,4 cm²

400

A circle has an area of 4π cm².  What is the radius?

2cm

500

A circle is inscribed in a square.  What percent of the square is covered by the circle?

Pi/4, which is about equal to 79%

Uttryck

100

Evaluate the expression 5y + 11 for y = 3

26

200

Write two expressions for “one eighth of x.”

x/8 and 0,125x

300

Simplify:

5(2x - 6) - (4x - 7)

6x - 23

400

Which figure in the following sequence has the value 900?

10, 20, 30, 40, 50...

The 90^th term

500

Write an expression for the n^th term of the following sequence:

2, 9, 28, 65, 126, 217

n³ + 1

Prisms and Pyramids

100

What is the formula for the volume of a prism?

V = Bh

200

What is the formula for the volume of a pyramid?

V = Bh/3

300

Find the surface area for a cube with a volume of 1000 mm³.

6 x 10 x 10 = 600 mm²

400

Two rectangular prisms are made of the same material.  They are the same height, but the side lengths of the larger prism's base are twice as long as the small prism's.  How many times heavier is the large prism?

It is 4 times heavier.

500

An architect is designing a two-part glass sculpture.  Part A is a rectangular prism (a box).  Part B is a rectangular pyramid that sits perfectly on top of a base identical to the prism.

• The shared base has a length of 50 cm and a width of 40 cm.  Both the prism and the pyramid have a height of 60 cm.

The architect needs to fill both shapes with a colored liquid. How many liters of liquid are needed in total to fill the entire sculpture (Prism + Pyramid)?

160 Liters

Enheter för volym

100

What is the cubic unit for 1 Liter?

1 dm³

200

Write 2 dm³ in mL

2 000 mL

300

You have a cylindrical container with a base area of 4π cm² and a height of 10 cm.  About how many whole mL will the container hold?

126 cm³ is equal to 126 mL.

400

An engineer is designing a precision glass cube to house a rare species of jellyfish. Each side of the cube measures exactly 40 centimeters.  Calculate the volume of the cube in Liters.

64 Liters

500

A chemical plant uses a large conical funnel to store liquid reactant. The funnel has a radius of 30 cm and a height of 70 cm.  How many liters with the cone hold?  Round to the nearest tenth.

65,9 L

Cylinders, cones and spheres

100

Draw the net of a cylinder.

(two circles and a rectangle)

200

What is the formula for the volume of a sphere?

V =  (4/3) x pi x r³

300

Find the volume for a cone with diameter 10cm and height 8cm.  Leave your answer in terms of pi.

800pi cm³

400

You are the owner of a tennis ball factory and are choosing between a cylindrical box and normal rectangular prism box.  Both boxes can fit exactly 3 tennis balls of diameter 6cm.  Which box should you choose?  Support your answer with calculations.

SA for the cylinder = 2(9pi) + 18(6pi) is about equal to 56,52 + 339,12 = 395,64 cm²

SA for the rectangular prism = 2(6 x 6) + 4(18 x 6) = 72 + 432 = 504 cm²

You should choose the cylindrical box because uses less material and holds the same number of balls.

500

A sphere is placed inside a cylinder with the same diameter and height.  What percent of the cylinder's volume is taken up by the sphere.  Use the formulas for volume and algebra to solve.  Round to the nearest whole percent.

2/3 is about equal to 67%