Prisms are 3-dimensional solids that have the same cross-section (the shape of its base or end) all the way through. For example, a rectangular prism has the same rectangle shape at both ends; a triangular prism has the same triangle shape at both ends; and a cylinder (a circle-based prism) has the same circle shape at both ends.
Volume is the amount of solid inside an object and is measured in cubic units (e.g. cubic metres and cubic centimetres).
Capacity is the amount of gas or liquid inside an object and is measured in litres and millilitres.
The general rule to calculate the volume of a prism is:
Volume of Prism = Area of Cross-section × Height
To convert from volume to capacity, it is important to know that:
Examples of Volume and Capacity are:
To change:
IF YOU CUBE THE NAME, YOU CUBE THE NUMBER.
Fettuccine is pasta with a rectangular prism shape. It is like flat spaghetti. Each piece is 10 mm wide, 300 mm long and 2 mm thick. What is amount of pasta needed to make one piece?
Answer:
The cross-section of a rectangular prism is a rectangle.
Take care not to mix up the height measurements.
Volume of Prism
= Area of Cross-section × Height
= Area of Rectangle × Height
= (L × H) × Height
= (10 × 2) × 300
= 6000 mm3 of fettuccine
A restaurant's take-away box (with lid) is to be designed to hold 600 cubic centimetres of food. A rectangular prism is easier to store. The smallest surface area would mean less material and therefore lower cost. What are the optimal (best) dimensions for this box?
A coffee mug is a circle-based prism or cylinder shape.
This mug's diameter is 7 cm. The height is 10 cm. What is the capacity of coffee in a full mug? (Use π = 3.14.)
Answer:
The cross-section of a cylinder is a circle.
Volume of Prism
= Area of Cross-section × Height
= Area of Circle × Height
= π r2 × H
= 3.14 × 3.5 × 3.5 × 10
= 384.65 cm3
= 384.65 millilitres of coffee
Each piece of macaroni has a larger diameter of 5 mm and a small diameter of 3 mm. The length of each piece is 10 mm.
What volume of pasta is needed to make one piece?
(Use π = 3.14.)
Answer:
The cross-section of macaroni is an annulus (a large circle minus a small circle).
Area of Cross-section
Area of large circle
= π R2
= 3.14 × 5 × 5
78.5 mm2
Area of small circle
= π r2
= 3.14 × 3 × 3
28.26 mm2
Area of annulus
= 78.5 – 28.26
=50.24 mm2
Volume
= Area of Cross-section × Height
= 50.24 × 10
= 502.4 mm3 of macaroni
(Would it have been easier to break the window?)
Helioculture is the process to make hydrocarbon-based fuel from genetically modified photosynthesizing bacteria from waste water (from baths and washing machines), carbon dioxide, nutrients and sunlight. According to manufacturer "Joule Unlimited", this alternative to crude oil can be produced at 19000 cubic metres per square kilometre and will be cost-effective when crude oil costs US$50 per barrel (or $310 per cubic metre). Currently, crude oil costs about US$95 per barrel.
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