Circles
The radius of a circle is 3 m. What is the area of the circle? Keep two decimal places.
28.27 m2
The volume formula of any cylinders.
V =Ah = ๐ฟr2h
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= 2๐ฟr = 10๐ฟ --> l= 10๐ฟ +3
SA = 2๐ฟr2+ Ch
= 50๐ฟ+(10๐ฟ+3)(12)
= 579.071 cm2
Avery needs 580cm2 wrapping paper.
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)
Vnew = 432 ๐ฟ = 1357.2 cm3
Yes, the new coffee cup is big enough.
The radius of a circle is 2 m. What is the circumference? Round your decimal to the nearest centimeter.
12.57 m
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 ยฝ of the radius is 2 cm. What is the volume? (Ben-M)
r = 4 cm
h= 12 cm
V= 603 cm3
When you look at the formula for surface area of any cylinder: 2๐๐โ+2๐๐2, what does the term 2๐๐2 represent?
It represents the area of the two circular faces.
When you look at the formula for surface area of any cylinder: 2๐๐โ+2๐๐2, what does the term 2๐๐โ represent?
It represents the curved surface area.
The area of a circle is 78.5 square meters. What is the radius of the circle?
5.0 m
In one cylinder, its height is 7 cm, and its volume is 637.8 cm3. What is its radius?
r = 5.4 cm
What are three expressions to find the surface area of cylinders?
SA = ๐ฟr2 + ๐ฟr2 + (C x h) = 2๐ฟr2+ (C x h)
SA =2๐ฟr2 + 2๐ฟrh =๐ฟr2 +๐ฟr2+ 2๐ฟrh
SA =2๐ฟ(d/2)2 +๐ฟdh = ๐ฟ(d/2)2 +๐ฟ(d/2)2 +๐ฟdh
Tripling the dimensions (r and h) of this cylinder. What does the volume change?
The volume will be increased by a factor of 27.
The formula for circumference of circle when diameter is given.
The formula for circumference of circle when radius is given.
C = ๐ฟd
C = 2๐ฟr
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(๐ฟ r2h) = 4.4L
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 โs box has a height of 8 cm and a diameter of 4 cm. Friend # 2โs box had a height of 6.5 cm and a radius of 3 cm. Whose box has a bigger surface area? (Lila)
Friend#1: 40๐ฟ = 125.66cm2
Friend#2: 57๐ฟ = 179.07 cm2
Friend#2's box has a bigger surface area.
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= 4๐ฟ +1.5 = 14.1 cm
w = 20 - 2(0.5) =19 cm
Dimension: 14.1cm x 19 cm
Area: 267.3 cm2
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
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=๐ฟ r2h = ๐ฟ (2)2(30)(6)=2262 cm3
Or,
V = Vbox - Vpaper + Vinner roll = 7824cm3
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= 150๐ฟ = 471.23cm2
Joe will need 472 cm2 of wrapping paper.
The โToothpickerโ 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?
Vbox = 3.8 x 2.1 x 6.1 = 48.678 cm3
Vcylinder = ๐ฟ r2h = ๐ฟ (2.7/2)2(6.1) = 34.926 cm3
V = Vbox-Vcylinder = 13.75= 13.8 cm3