Note: use Q1 and Q5 from surface area of 3D shapes
Surface Area of 3D Shapes FSQ2
The following 3D shape consists of a cylinder on top of a cube.
Calculate the surface area of the 3D shape.
Give your answer to 2 decimal places.
Answer type: simple
Answer: 403.9 cm^2
Workings:
The total surface area can be calculated by working out the surface area of the cube (including the covered section, as this is the same as the area of the top of the cylinder) and the curved face of the cylinder.
The surface area of a cube with a side length of 7 cm is 7\times7\times6=294 cm^2
The area of the curved face of the cylinder is 5\times3.14\times7=109.9 cm^2
So the total area is 294+109.9=403.9 cm^2
3 marks
Surface Area of 3D Shapes FSQ3
A square bipyramid is a 3D shape which can be constructed from identical triangles, as shown in the diagram below.
Using the above diagram, calculate the surface area of the square bipyramid.
Answer type: simple
Answer: 128 cm^2
Workings:
The area of one triangular face is \dfrac{1}{2}\times \text{base}\times \text{hight}=\dfrac{1}{2}\times4\times8=16 cm^2
The square bipyramid consists of 8 triangular faces, so the total area is 8\times16=128 cm^2
2 marks
Surface Area of 3D Shapes FSQ4
A 3D model of a house is shown below.
Calculate the surface area of the model, assuming the highest point of the roof is in the centre of the building.
Answer type: simple
Answer: 672 cm^2
Workings:
Start by working out the surface area of the two slanted faces (the roof). Their combined area is 2\times(10\times8) = 160 cm^2
Next, calculate the area of the two triangular sections. Their combined area is 2\times \bigg(\dfrac{1}{2}\times16\times6\bigg)=96 cm^2
The front and back sides of the model (according to the diagram) have a combined area of 2\times(6\times16)=192 cm^2
The left and right sides of the model have a combined area of 2\times(6\times8)=96 cm^2
Finally, the base of the model has an area of 16\times8=128 cm^2
So the total surface area of the model is:
160+96+192+96+128=672 cm^2
4 marks
Surface Area of 3D Shapes FSQ6
Below is a diagram of a square-based pyramid.
Calculate the surface area of the pyramid.
Answer type: simple
Answer: 39 m^2
Workings:
The area of one triangle face is \dfrac{1}{2}\times\text{base}\times\text{height}=\dfrac{1}{2}\times3\times5=7.5 cm^2
The combined area of all four triangle faces is therefore 4\times7.5=30 cm^2
The area of the square base is 3\times3=9 cm^2
The total area is therefore 30+9=39 cm^2
3 marks