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Lesson 10 of 11

9 min

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Eight questions, one idea each. Keep the table beside you.

Surface areas and volumes — what to count
MoveHow it goes
Name the solidsFind each basic solid and the join.
Area or volumePaint and cloth ask for area. Water and air ask for volume.
The joinTouching parts are inside. Do not count them.
The tentCanvas is the curved parts. Read if the ground is covered.
The hollowTake off the mouth. Add the bowl.
The slantOn a hemisphere: cone height = total height − radius. Then l² = r² + h².
The jobList the faces the job counts.
Start to finishRead, split, find, pick, compute, answer.

A tent has a pointed roof on round walls. Which basic solids make it?

  • A cone on a hemisphere
  • A cone on a cylinder
  • A cylinder on a hemisphere

How much water can a toy hold?

  • Its surface area, in square units
  • Both, added together
  • Its volume, in cubic units

A toy has cone skin 2310 and cone base 1386. It has dome skin 2772 and flat face 1386. What is the paint area?

  • 5082
  • 7854
  • 6468

A tent has cone skin 550 and drum wall 440. The ground circle is 154. The ground is not covered. How much canvas is needed?

  • 1144
  • 154
  • 990

A block has surface area 952. A hemisphere bowl of radius 7 is cut in its top. Find the new surface area.

  • 1414
  • 1106
  • 1260

A toy is a cone on a hemisphere. Its radius is 21 and its total height is 49. How tall is the cone?

  • 28
  • 49
  • 70

Which faces make the surface of a capsule? It is a cylinder with a hemisphere at each end.

  • 2 domes, the tube wall and 2 circles
  • Both domes and the tube wall
  • One dome and the tube wall

You have found the missing length of a solid. What comes next?

  • Write the answer at once
  • Split the object into its solids
  • Pick the faces the job counts

This is Chapter 12, Surface Areas and Volumes, in your book. Try its exercises next.

Next: Statistics. It gives one table and three averages.

Reveal every answer to finish this lesson.