Surface area and volume review

key notes :

โœˆ๏ธ Surface area of a sphere:

Surface area = 4โ€‹๐œ‹r2 

A rectangular prism has 3 pairs of identical faces. Each face is a rectangle.

Volume = length ร— width ร— heigh

Learn with an example

๐Ÿ“š What is the surface area of this sphere?

๐Ÿ“š Use โ€‹๐œ‹ โ‰ˆ 3.14 and round your answer to the nearest hundredth.

_______square centimetres

  • Find the radius of the sphere.radius = 
12 ร— diameter = 12 ร— 14 = 7
  • Use this number in the surface area formula. Use โ€‹๐œ‹ โ‰ˆ 3.14.
  • Surface area = 4โ€‹๐œ‹r2
  •  โ‰ˆ 4 ร— 3.14 ร— 72
  •  โ‰ˆ 615.44The surface area of the sphere is about 615.44 square centimetres.

๐Ÿ“š What is the volume?

________ cubic millimetres.

  • Find the base, height, and length of the triangular prism.
  • base: 12 mm
    height: 7 mm
    length: 6 mm
    Use these numbers in the volume formula.
Volume = 12 ร— base ร— height ร— length
 = 12 ร— 12 ร— 7 ร— 6
 = 252
  • The volume is 252 cubic millimetres.

๐Ÿ“š The surface area of this cone is 414.48 square millimetres. What is the slant height of this cone?

๐Ÿ“š Use โ€‹๐œ‹ โ‰ˆ 3.14 and round your answer to the nearest hundredth.

s โ‰ˆ _______ millimetres

  • Find the surface area and radius of the cone.
    surface area = 414.48
    radius = 6
    Find the area of the base. Use โ€‹๐œ‹ โ‰ˆ 3.14.
    Area of base = โ€‹๐œ‹r2
     โ‰ˆ 3.14 ร— 62
     โ‰ˆ 113.04
  • Find the lateral area.
    Lateral area = โ€‹๐œ‹rs
     โ‰ˆ 3.14 ร— 6 ร— s
     โ‰ˆ 18.84s
  • Now add the areas to find the slant height of the cone.
Surface area = B + L.A.
414.48 โ‰ˆ 113.04 + 18.84s
414.48 โˆ’ 113.04 โ‰ˆ 18.84s
301.44 โ‰ˆ 18.84s
301.44 รท 18.84 โ‰ˆ s
16 โ‰ˆ s
  • The slant height of the cone is about 16 millimetres.

Let’s practice!