Review Competition

Circles

100

The radius of a circle is 3 m. What is the area of the circle? Keep two decimal places.

28.27 m²

200

The radius of a circle is 2 m. What is the circumference? Round your decimal to the nearest centimeter.

12.57 m

300

The area of a circle is 78.5 square meters. What is the radius of the circle?

5.0 m

400

The formula for circumference of circle when diameter is given.

The formula for circumference of circle when radius is given.

C = 𝝿d

C = 2𝝿r

500

Alex has a circular carpet in his drawing room. He wants to put a circular table in middle of the carpet. The diameter of the carpet is 1.2 meters and the radius of the table is 0.4 meters. Calculate how much area of carpet is left after putting the table in place? Use 3.14 for pi. Convert your answer to cm²

0.6280 m²

0.6280 m² x 10000cm²/m² =6280.0 cm²

Volume of cylinders

100

The volume formula of any cylinders. 

V =Ah = 𝝿r²h

200

Jimmy went to the store and found a can of coca-cola. Jimmy asked Ben to find the volume of the coke can, if the height of the can is 12 cm and ½ of the radius is 2 cm. What is the volume? (Ben-M)

r = 4 cm

h= 12 cm

V= 603 cm³

300

In one cylinder, its height is 7 cm, and its volume is 637.8 cm³. What is its radius?

r = 5.4 cm

400

A can of soup is 10.3 cm high and its diameter is 6.7 cm. A box that is shipped to the grocery store contains 12 cans each. What volume of soup is in the box, in litres?

V= 12(𝝿 r²h) = 4.4L

500

Paper towels are sold in boxes of 6 rolls. Each roll is a cylinder with a height of 30cm and an outer diameter of 12 cm. If the inner diameter of each roll is 4 cm, how much wasted space is there in the box? (Assume the box is made to just fit the paper towels).

V=𝝿 r²h = 𝝿 (2)²(30)(6)=2262 cm³

Or,

V = V_box - V_paper + V_{inner roll =} 7824cm³

Surface area of cylinder

100

Avery has a gift for her friend. The cylindrical box has dimensions r = 5cm, and h= 12 cm. How much wrapping paper will Avery need if there is a 3-cm overlap to tape the gift? 

C= 2𝝿r = 10𝝿 --> l= 10𝝿 +3

SA = 2𝝿r²+ Ch

     = 50𝝿+(10𝝿+3)(12)

     = 579.071 cm²

Avery needs 580cm² wrapping paper. 

200

When you look at the formula for surface area of any cylinder: 2𝜋𝑟ℎ+2𝜋𝑟², what does the term 2𝜋𝑟² represent?

It represents the area of the two circular faces.

300

What are three expressions to find the surface area of cylinders? 

SA = 𝝿r² + 𝝿r² + (C x h) = 2𝝿r²+ (C x h)

SA =2𝝿r² + 2𝝿rh =𝝿r² +𝝿r²+ 2𝝿rh

SA =2𝝿(d/2)² +𝝿dh = 𝝿(d/2)² +𝝿(d/2)² +𝝿dh

400

Two friends decide to buy two boxes of pringles. Friend #1 says that the surface area of her box is bigger. Friend #2 disagrees and says that his box is bigger. Friend #1 ‘s box has a height of 8 cm and a diameter of 4 cm. Friend # 2’s box had a height of 6.5 cm and a radius of 3 cm. Whose box has a bigger surface area? (Lila)

Friend#1: 40𝝿 = 125.66cm²

Friend#2: 57𝝿 = 179.07 cm²

Friend#2's box has a bigger surface area.

500

Joe bought his friend a poster for his birthday, and he wants to know how much wrapping paper he needs to cover the cylindrical gift with a height of 10 cm and a radius of 5cm. How much wrapping paper does he need in total? (Charlotte H)

SA= 150𝝿 = 471.23cm²

Joe will need 472 cm² of wrapping paper. 

Mixed question

100

Ava wants to buy a new coffee cup that will hold more coffee. The one she currently uses is about 785.4 cm³. The new coffee cup has a radius of 6 cm and a height of 12 cm. Is the new one she wants big enough? (Avery W)

V_new = 432 𝝿 = 1357.2 cm³

Yes, the new coffee cup is big enough.

200

When you look at the formula for surface area of any cylinder: 2𝜋𝑟ℎ+2𝜋𝑟², what does the term 2𝜋𝑟ℎ represent?

It represents the curved surface area.

300

Tripling the dimensions (r and h) of this cylinder. What does the volume change? 

The volume will be increased by a factor of 27.

400

We are creating the label for a 20cm tall soup can with a radius of 2cm. We need a 1.5 cm overlap for the label to be glued to itself, and the label will be one half of a cm from each edge of the can. What size of paper (what are the dimensions?) will we need?

l= 4𝝿 +1.5 = 14.1 cm

w = 20 - 2(0.5) =19 cm

Dimension: 14.1cm x 19 cm

Area: 267.3 cm²

500

The “Toothpicker” Company sells toothpicks in boxes and in cylindrical containers. Each box is 3.8 cm by 2.1 cm by 6.1 cm and each cylinder is 6.1 cm high and 2.7 cm in diameter. Which package has a bigger inside space? How much more space does it contain?

V_box = 3.8 x 2.1 x 6.1 = 48.678 cm³

V_cylinder = 𝝿 r²h = 𝝿 (2.7/2)²(6.1) = 34.926 cm³

V = V_box-V_cylinder = 13.75= 13.8 cm³