Prisms - Intermediate and Higher tier
A prism is a 3D shape which has a constant cross section. This means that both ends of the solid are the same shape. If you cut anywhere along the length of the prism parallel to these ends the shape will always be the same.
This formula is given to you in the exam.
To calculate the area of the cross section you will need to be familiar with calculating the area of 2D shapes.
Question
Calculate the volume of this trophy, when the area of cross section is 55 cm2 and the thickness is 12 cm.
\(\text{Volume = area of cross section 脳 length}\)
Volume = 55 脳 12 = 660 cm3
Question
A tin of soup has a radius of 3.75 cm and a height of 11 cm.
Calculate the volume of soup in the tin. Give your answer to the nearest millilitre (1 cm3 = 1 ml).
For the purposes of this question you can ignore the thickness of the tin.
\(\text{Area of cross section} = 蟺 \times r^2\)
Area of cross section = \({蟺}\) x 3.752 = 44.17864669 cm2
\(\text{Volume = area of cross section} \times \text{length}\)
Volume = 44.17864669 x 11 = 485.9651136 cm3
Volume = 486 ml (nearest ml)
To visualise the surface area of a prism, we can think about the net of the shape.
There are two faces and a rectangular section measuring the length of the prism by the perimeter of the cross section.
To calculate the surface area of a prism, use the following formula:
\(\text{2} \times \text{area of cross section} ~+~ \text{(perimeter of cross section} \times \text{length)}\)
Question
Juan is comparing the amount of paper needed to wrap each of his Christmas presents.
Calculate the surface area of this equilateral triangular prism:
\(\text{Area of the cross section of a triangle} ~=~ \frac {1} {2} \times \text{base} \times \text{height}\)
Area of cross section = 陆 脳 5 脳 4.3 = 10.75 cm2
Perimeter of cross section = 5 + 5 + 5 = 15 cm
Area of sides = perimeter of cross section 脳 length = 15 脳 12 = 180 cm2
Total surface area = 10.75 + 10.75 + 180 = 201.5 cm2
Question
The base and curved surface of a tin are to be covered to create a pen pot. Calculate the area that will be covered when using a cylinder with a radius of 3.75 cm and a height of 11 cm.
\(\text{Area of base} = 蟺 \times r^2\)
Area of base = \({蟺}\) x 3.752 = 44.17864669 cm2
\(\text{Circumference of a circle} = 2~蟺~r\)
Circumference of a circle = 2 x \({蟺}\) x 3.75 = 23.5619449 cm
\(\text{Area of outside face = circumference 脳 length}\)
Area = 23.5619449 脳 11 = 259.1813939 cm2
Total area = 44.17864669 + 259.1813939 = 303.3600406 cm2
Total area = 303.36 cm2 (to two decimal places)
More guides on this topic
- Loci and constructions - WJEC
- Pythagoras' theorem - Intermediate & Higher tier - WJEC
- Trigonometry 鈥 Intermediate & Higher tier - WJEC
- Enlargements/Similar shapes - Intermediate & Higher tier - WJEC
- Maps - WJEC
- Conversion between metric and imperial units - WJEC
- Dimensional analysis - Intermediate & Higher tier - WJEC
- Compound measures - WJEC
- Perimeter and area - WJEC
- Video playlist