A composite solid consists of a triangular prism which fits exactly on top of a cube, as shown - HSC - SSCE Mathematics Standard - Question 25 - 2020 - Paper 1
Question 25
A composite solid consists of a triangular prism which fits exactly on top of a cube, as shown.
Find the surface area of the composite solid.
Worked Solution & Example Answer:A composite solid consists of a triangular prism which fits exactly on top of a cube, as shown - HSC - SSCE Mathematics Standard - Question 25 - 2020 - Paper 1
Step 1
Calculate the Area of the Triangular Face
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Answer
First, we determine the height of the triangular face of the prism. The height can be calculated as follows:
Height = 11 cm - 8 cm = 3 cm.
Now, we can calculate the area of the triangular face using the formula:
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Answer
The cube has five visible square faces, where each face has an area of:
Area of one square face = ( 8 \times 8 = 64 , cm^2 ).
Thus, the total area of the five square faces is:
Total area = ( 5 \times 64 = 320 , cm^2 ).
Step 3
Calculate the Area of the Rectangular Faces
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Answer
Next, we calculate the area of the two rectangular faces of the prism. The dimensions for each rectangular face are 5 cm (height) and 8 cm (length). Therefore, the area of one rectangular face is:
Area = ( 5 \times 8 = 40 , cm^2 ).
As there are 2 rectangular faces:
Total area = ( 2 \times 40 = 80 , cm^2 ).
Step 4
Calculate the Total Surface Area
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Answer
Finally, we combine the areas calculated above:
Total surface area = Area of cube faces + Area of triangular faces + Area of rectangular faces = 320 + 12 + 80 = 412 ; cm^2.
