Aussie Maths & Science Teachers: Save your time with SmarterEd
The surface area of a brick is given by the rule:
total surface area = 2 × [(width × height) + (width × length) + (height × length)]
The brick shown has a total surface area of 982 square centimetres.
What is the width of the brick?
centimetres |
`10.5\ text(cm)`
`text(Let)\ \ w = text(width of the brick)`
`text(Surface Area)` | `= 2 xx [8w + 22w + (8 xx 22)]` |
`982` | `= 2(30w + 176)` |
`= 60w + 352` | |
`60w` | `= 630` |
`:. w` | `= 10.5\ text(cm)` |
The surface area `(S)` of the prism below can be calculated by multiplying the perimeter of its face `(p)` by its height `(h)`, and adding twice the area of its face `(F)`.
Which one of these formulas could be used for this calculation?
|
`S = 2 p h F` |
|
`S = p h + F` |
|
`S = p h + 2F` |
|
`S = 2 ph + 2F` |
`S = p h + 2F`
`S = p h + 2F`
A cube has a side length of 6 cm.
Two smaller cubes of side length 3 cm are attached to the larger cube as shown in the diagram below.
What is the surface area of the new object?
`216\ text(cm²)` | `243\ text(cm²)` | `270\ text(cm²)` | `288\ text(cm²)` |
|
|
|
|
`270\ text(cm²)`
`text(One strategy:)`
`text{Calculate the surface area (S.A.) of the 2 objects joined}`
`text(separately and deduct the area where they join.)`
`text{S.A. (large cube)} = 6 xx 6xx 6 = 216\ text(cm²)`
`text{S.A. (2 smaller cubes joined together)}`
`=2 xx (3 xx 3) + 4 xx (6 xx 3)`
`=90\ text(cm²)`
`text{S.A. to be deducted (where cubes are attached)}`
`= 2 xx (6 xx 3)`
`= 36\ text(cm²)`
`:.\ text{S.A. (new object)}` | `= 216 + 90 – 36` |
`=270\ text(cm²)` |
The rectangular prism, shown below, is cut in half to form 2 equal cubes.
What is the ratio of the surface area of the rectangular prism to one of the cubes?
`3 : 5` | `5 : 3` | `1 : 2` | `2 : 1` |
|
|
|
|
`5 : 3`
`text(S.A. of rectangular prism)`
`= 2 xx (h xx h) + 4 xx (2h xx h)`
`= 2h^2 + 8h^2`
`= 10 h^2`
`text(S.A. of cube)`
`= 6 xx (h xx h)`
`= 6h^2`
`:.\ text(Ratio of rectangular prism to cube)`
`= 10h^2 : 6h^2`
`= 5 : 3`
A glass aviary is made up of four triangles and a square, as shown in the diagram below.
Harry is hired to clean the interior sides of the aviary, not including the floor.
What is the area that Harry will need to clean?
m² |
`402\ text(m²)`
`text(Area to clean)`
`= 4 xx 1/2 bh`
`= 4 xx 1/2 xx 15 xx 13.4`
`= 402\ text(m²)`