CBSE Math Revision Start revising
Themed maths

Spring egg geometry for CBSE Class 10

A ready-to-teach lesson for spring: model eggs with combinations of solids, melt and recast chocolate, and pack an egg in a box. A 5-minute starter, a 35-minute main activity, an extension and full worked answers. No calculator; use π = 22/7.

Level
CBSE Class 10 (Class 9 can try most of it)
Time
40 minutes, plus a 10-minute extension
Topics
Surface areas and volumes: combinations of solids; Converting one solid to another; Volume and surface area of spheres, hemispheres, cones and cubes
Equipment
No calculator. Use π = 22/7 throughout.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A12 minA hemisphere-and-cone egg
Main: task B12 minMelt and recast
Main: task C11 minAn egg in a box
Extension10 minFast finishers or homework

Starter (5 minutes)

Quick-fire mental maths. Use π = 22/7.

  1. Find the curved surface area of a hemisphere of radius 7 cm. (Use π = 22/7.)
  2. Find the volume of a cone of radius 7 cm and height 6 cm. (Use π = 22/7.)
  3. Find the slant height of a cone with radius 6 cm and height 8 cm.
  4. Find the surface area of a sphere of radius 7 cm. (Use π = 22/7.)

Main activity (35 minutes)

Task A: A hemisphere-and-cone egg (12 min)

A wooden egg is a hemisphere of radius 7 cm joined to a cone of radius 7 cm and height 24 cm. Use π = 22/7.

  1. Find the volume of the egg.
  2. Find the total surface area of the egg.
  3. The egg is painted at ₹0.50 per cm2. Find the cost.

Task B: Melt and recast (12 min)

Use π = 22/7.

  1. A solid chocolate sphere of radius 7 cm is melted and made into small spheres of radius 1.75 cm. How many small spheres are made?
  2. A cylinder of radius 7 cm and height 20 cm is full of melted chocolate. It is poured into hemispherical moulds of radius 3.5 cm. How many moulds can be filled completely?
  3. Find the surface area of one small sphere of radius 3.5 cm, to wrap it in foil.

Task C: An egg in a box (11 min)

A spherical chocolate egg of radius 3.5 cm fits exactly inside a cube-shaped box of side 7 cm. Use π = 22/7.

  1. Find the volume of empty space in the box.
  2. What fraction of the box does the egg fill?
  3. The box has no lid. Find the area of card needed to make it.

Extension (10 minutes)

For fast finishers, or as homework.

  1. An egg is a hemisphere of radius 7 cm on a cone of radius 7 cm. What height must the cone have for the cone and the hemisphere to have equal volumes?
  2. How many spheres of radius 1 cm can be made by melting a sphere of radius 5 cm? What is the ratio of the total surface area of the small spheres to that of the big sphere?

For teachers

Teacher notes and full worked answers
  • These are typical ‘combination of solids’ and ‘conversion of solids’ questions in a spring setting.
  • In task A (b), remind students that the flat circle where the two solids join is inside the egg, so it is not painted.
  • In task B (b), insist on complete moulds: 34, not 34.28.

Starter

  1. 308 cm2
    • 2 × 22/7 × 7 × 7 = 308
  2. 308 cm3
    • 1/3 × 22/7 × 49 × 6 = 308
  3. 10 cm
    • √(36 + 64) = 10
  4. 616 cm2
    • 4 × 22/7 × 49 = 616

Task A: A hemisphere-and-cone egg

  1. 5852/3 = 1950 2/3 cm3
    • Hemisphere: 2/3 × 22/7 × 343 = 2156/3.
    • Cone: 1/3 × 22/7 × 49 × 24 = 1232.
    • 2156/3 + 1232 = 5852/3
  2. 858 cm2
    • Slant height = √(49 + 576) = 25.
    • Hemisphere: 2 × 22/7 × 49 = 308. Cone: 22/7 × 7 × 25 = 550.
    • 308 + 550 = 858
  3. ₹429
    • 858 × 0.5 = 429

Task B: Melt and recast

  1. 64
    • (7/1.75)3 = 43 = 64 (the 4/3 × π cancels).
  2. 34
    • Cylinder: 22/7 × 49 × 20 = 3080 cm3.
    • Mould: 2/3 × 22/7 × 42.875 = 539/6 cm3.
    • 3080 ÷ 539/6 = 18 480/539 = 34.28…, so 34 moulds.
  3. 154 cm2
    • 4 × 22/7 × 3.5 × 3.5 = 154

Task C: An egg in a box

  1. 490/3 = 163 1/3 cm3
    • Cube: 343. Sphere: 4/3 × 22/7 × 42.875 = 539/3.
    • 343 − 539/3 = 490/3
  2. 11/21
    • (539/3) ÷ 343 = 539/1029 = 11/21
  3. 245 cm2
    • 5 faces × 49 = 245

Extension

  1. 14 cm
    • 1/3 × π × 49 × h = 2/3 × π × 343 gives 49h = 686, so h = 14.
  2. 125; 5 : 1
    • (5/1)3 = 125
    • 125 × 4π × 1 : 4π × 25 = 500π : 100π = 5 : 1

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

Practise the topics

Big tournament statistics maths · Eclipse geometry maths · Ada Lovelace Day maths · All themed maths

More for lessons: Weekly starters · Worksheet builder · Olympiad and competition maths · National Mathematics Day puzzles