Break it into basic solids
A new solid is made of solids you already know, so split it into them.
The oil tank on a truck
Oil is carried in a tank fitted on the back of a truck. It is not a cuboid, a cone or a sphere. It looks like this.
What is the tank made of?
What this lesson covers
The idea
A solid made by combining basic solids (cuboid, cone, cylinder, sphere, hemisphere) is handled by breaking it down into those basic solids, whose surface areas and volumes are already known.
The oil tank on a truck
Oil is carried in a tank fitted on the back of a truck. It is not a cuboid, a cone or a sphere. It looks like this.
What is the tank made of?
- A cylinder with a hemisphere at each end
- One big sphere
- A cuboid with a cone on top
Name the parts
A part of each solid is lit. Choose the basic solid that it is. When every part has a name, the solid falls apart.
Break it down
A combined solid is broken into basic solids (cuboid, cone, cylinder, sphere, hemisphere) whose surface areas and volumes we already know.
Whenever we meet a new problem, we first try to break it into smaller problems that we have already solved. The tank is a cylinder with two hemispheres. The top is a hemisphere on a cone. The rocket is a cone on a cylinder.
The next two lessons use this: find the surface area of the pieces that stay outside, and the volume of all the pieces together.
Notes
A combined solid is broken into basic solids (cuboid, cone, cylinder, sphere, hemisphere) whose surface areas and volumes we already know.
Check yourself
A test tube has a flat open end and a round closed end. Which basic solids is it made of?
How many basic solids make up the oil tank: a cylinder with a hemisphere at each end?
Answer: 3 solids
1 cylinder + 2 hemispheres = 3 basic solids.
A toy rocket is a cone placed on top of a cylinder. Which basic solids do we use to find its surface area or volume?
To find the surface area or volume of a solid that is not one of the basic solids, what do we try first?
- A cylinder and a hemisphere — correct. Yes! The straight part is a cylinder and the rounded bottom is half a ball, a hemisphere.
- A cylinder and a cone. A cone has a pointed end. The closed end of a test tube is round, not pointed.
- A cuboid and a sphere. A test tube has no flat faces except its open end, and the round end is only half a ball.
- A cone and a cylinder — correct. Yes! We find the cone and the cylinder separately, with the formulas we already know.
- Only a cylinder. The pointed top is a cone. It needs its own formulas.
- A sphere and a cuboid. The rocket has no ball and no box. It has a pointed top (a cone) on a round body (a cylinder).
- Break it down into basic solids that we know — correct. Yes! Break it into smaller problems that we have already solved.
- Look for a brand new formula for that exact shape. We do not need one. The pieces are basic solids with known formulas.
- Measure its surface with a string. Measuring is not needed. If we know the sizes of the parts, formulas give the answer.