Area of 2D Shapes
Determine the Area of a Square with 4.5cm side lengths
A = 4.5 x 4.5 = 20.25 cm2
The longest side of a right triangle is called the...
Hypotenuse
Calculate the surface area of a cube with 5.5 cm sides.
SA = 6 x 5.5 x 5.5
SA = 181.5 cm2
Calculate the volume of a cube with 81 yd side lengths.
V = 81 x 81 x 81 = 531 441 yd3
Determine the area of a rectangle with side lengths 2.4in. and 6.1in.
A = 2.4 x 6.1 = 14.64 in2
State the pythagorean theorem.
a2 + b2 = c2
Calculate the surface area of a rectangular prism with dimensions 1.1in by 2.2in by 3.3in.
SA = (2 x 1.1 x 2.2)+(2 x 1.1 x 3.3)+(2 x 2.2 x 3.3)
SA = 4.84 + 7.26 + 14.52
SA = 26.62 in2
Calculate the volume of a rectangular prism with dimensions 99 cm by 100 cm by 101 cm.
V = 99 x 100 x 101 = 999 900 cm3
Determine the area of a circle with a diameter of 18 meters.
r = 18/2 = 9 m
A = pi x 9 x 9 = 254.5 m2
The pythagorean theorem only works with what type of triangle?
A right triangle (90 degrees).
Calculate the SA of a cylinder with a radius of 11 mm and a height equal to the radius.
SA = (2 x pi x 11 x 11) + (2 x pi x 11 x 11)
SA = 760.27 + 760.27
SA = 1520.54 mm2
Calculate the volume of a cylinder with a height of 16 ft and a diameter of 50 ft.
Radius = 50/2 = 25 ft
V = pi x 25 x 25 x 16 = 31 415.93 ft3
Determine the side length of a square with an area of 64 in2.
The square root of 64in2 is 8 inches.
Side length = 8 in.
Determine the hypotenuse of a right angle triangle with legs 15cm and 20 cm.
c = sqrt(152 +202)
= sqrt(225 + 400)
= sqrt(625)
c = 25 cm
Calculate the SA of a sphere with a radius of 12 inches in square cm.
Radius = 12 in x 2.54 = 30.48 cm
SA = 4 x pi x 30.48 x 30.48 = 11674.54 cm2
Determine the relationship between cubic cm and cubic inches. Use this relationship to convert 3650 in3 to cm3.
1 in = 2.54 cm
1 in x 1 in x 1 in = 1 in3
2.54 cm x 2.54 cm x 2.54 cm = 16.39 cm3
1 in3 = 16.39 cm3
3650 in3 x 16.39 cm3/in3 = 59 823.5 cm3
A circle with a radius of 5cm is cut out of a piece of paper that measures 8.5" x 11". How much paper remains in square cm?
8.5 x 2.54 = 21.59 cm
11 x 2.54 = 27.94 cm
Area of paper: 21.59 x 27.94 = 603.22 cm2
Area of Circle: pi x 5 x 5 = 78.54 cm2
Area remaining = 603.22 - 78.54 = 524.68 cm2
A triangle has one leg of length 10 inches and a hypotenuse of length 26 inches. Determine the length of the missing leg.
b = sqrt(262 - 102)
= sqrt(676 - 100)
= sqrt(576)
b = 24 in
A square based pyramid has a base of 30 cm and a slant height of 25 cm. A cone has a radius of 15 cm and the same slant height as the pyramid. Which has the most surface area, and by how much?
SA Pyramid =(2 x 30 x 25)+(30 x 30) = 2400 cm2
SA Cone = (pi x 15 x 25) + (pi x 15 x 15)
SA Cone = 1178.10 + 706.86 = 1884.96 cm2
Pyramid has more SA.
SA Pyramid - SA Cone = 2400 - 1884.96
= 515.04 cm2
It costs $0.0015 per cm3 of milk. Determine the cost of a 4L jug of milk if 1L = 1000 cm3.
4L x 1000 = 4000 cm3 of milk in a jug
4000 cm3 x $0.0015/cm3 = $6.00