Surface Area
What is surface area?
Adding up all the areas of each of the faces/bases of a 3D shape. Surface Area is measured in squared units.
What is volume?
The amount of space that a 3D object occupies. Volume is measured in cubed units.
What is capacity?
The maximum quantity a container/object can hold or carry. Capacity can be measured in L, gallons, etc.
Calculate the Surface Area of a cube with a side length of 8 cm.
SA = s2 (6)
SA = (8)2 (6)
SA = 384 cm2
Find the volume of a rectangular prism that is 13 cm long, 16 cm wide, and 5 cm high.
V = lwh
V = (13)(16)(5)
V = 1040 cm3
What is the capacity of a cylinder with a volume of 5200 cm3 ?
C = ((5200)(1))/1000
C = 5.2 L
Calculate the surface area of a square based pyramid with a base length of 8 m and a height of 6 m.
SA = b2 + 2bs
a2+b2=c2
42+62=c2
c = 7.2 m = s
SA = 82 + 2(8)(7.2)
SA = 179.2 m2
Calculate the volume of a cone with a diameter of 5 m and a height of 6.5 m.
V = (πr2h)/3
V = (π(2.5)2 6.5)/3
V = 42.5 m3
What is the capacity of a rectangular prism with a volume of 645 ft3?
1 ft3 = 7.48 US gallons
645 ft3 = C
C = (645)(7.48)
C = 4824.6 US gallons
Calculate the lateral surface area of cylinder with a diameter of 10 cm and a height of 27 cm.
SA = 2πr2 + 2πrh
SA (lateral) = 2πrh
SA (lateral) = 2π(5)(27)
SA = 848.2 cm2
Calculate the height of a cylinder with a volume of 150 ft3 and a radius of 1.5 ft.
V = πr2h
150 = π(1.5)2(h)
150/(π (1.5)2) = h
21.2 ft = h
A hot-tub has a capacity of 84.7 L. What is the volume of the hot-tub?
1 L = 1000 cm3
84.7 L = V
V = (1000)(84.7)
V = 84,700 cm3
Calculate the total surface area of a math ice cream cone that consists of a perfect hemisphere and a cone. The radius is 15 cm and the slant height of the cone is 10 cm.
SA (hemisphere) = 3πr2
SA (hemisphere) = 2πr2 = 2π(15)2 = 1413.7 cm2
SA (cone) = πr2 + πrs
SA (cone) = πrs = π(15)(10) = 471.2 cm2
SA (total) = 1413.7 + 471.2
SA (total) = 1884.9 cm2
How many 190,000 cm3 puppies can fit in a rectangular-based prism play-pen measuring 2.8 m by 1.7 m by 0.8 m?
V = lwh
V = (2.8)(1.7)(0.8)
V = 3.8 m3 or 3.81 m3
1 m = 100 cm
1 m3 = (100 cm)3
1 m3 = 1,000,000 cm3
1 m3 = 1,000,000 cm3
3.8 m3 = ?
(3.8)(1,000,000 cm3) = 3,800,000 cm3
3,800,000 cm3/190,000 cm3 = 20 puppies!
A pyramid has a volume of 650 m3. If the pyramid is 40% full of sand, how many litres of sand is it holding?
(0.40)650 m3 = 260 m3
1 m = 100 cm
1 m3 = (100 cm)3
1 m3 = 1,000,000 cm3
1 m3 = 1,000,000 cm3
260 m3 = ?
(260)(1,000,000) = 260,000,000 cm3
1000 cm3 = 1 L
260,000,000 cm3 = C
C = (260,000,000)/(1000)
C = 260,000 L