Introduction: Similar to surface area, this is another formula-based lesson. The challenges are the same: using Pythagoras, dealing with composite solids, and solving "recasting" problems where the volume of one shape is used to find a dimension of another.

The "S Pass" Foundation (නියත S එකකට)

• Prompt 1 (Formula): Write down the formula for the volume of a square-based right pyramid.

• Prompt 2 (Formula): Write down the formula for the volume of a right circular cone.

• Prompt 3 (Formula): Write down the formula for the volume of a sphere.

• Prompt 4 (Calculate): Find the volume of a cone with radius 7 cm and height 12 cm.

• Prompt 5 (Calculate): Find the volume of a sphere with radius 21 cm.

  
  

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Problem Solve): A square-based pyramid has a base side of 12 cm and a slant height of 10 cm. Find its perpendicular height and then calculate its volume.

• Prompt 2 (Problem Solve): A cone has a base diameter of 10 cm and a slant height of 13 cm. Find its volume.

• Prompt 3 (Problem Solve): The volume of a sphere is 3500​π cm³. Find its radius.

• Prompt 4 (Problem Solve): Find the volume of a solid hemisphere of radius 6 cm.

• Prompt 5 (Recasting): A solid metal sphere of radius 3 cm is melted and recast into a solid cone of height 3 cm. What is the radius of the cone's base?

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Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Problem Solve): The volume of a square-based right pyramid is 320 cm³. If its perpendicular height is 15 cm, find the length of a side of its base.

• Prompt 2 (Composite Solid): A solid is formed by a cylinder of height 10 cm and radius 7 cm, with a hemisphere of the same radius on top. Find the total volume of the solid.

• Prompt 3 (Comparison): How many spherical lead shots of diameter 1 cm can be made from a solid cuboid of lead measuring 11 cm x 10 cm x 7 cm?

• Prompt 4 (Application): A conical flask of radius 6 cm and height 8 cm is completely filled with water. This water is poured into a cylindrical flask of radius 4 cm. Find the height of the water in the cylindrical flask.

• Prompt 5 (Ratios): If the ratio of the radii of two spheres is 2:3, what is the ratio of their volumes?

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Securing the "A" Distinction (A සාමාර්ථය තහවුරු කරගන්න)

• Prompt 1 (Challenge): A container is in the shape of an inverted cone of height 21 cm and base radius 12 cm. It is filled with water up to half its height. Find the volume of the water. (Hint: Use similar triangles to find the radius of the water surface).

• Prompt 2 (Derive): A sphere is placed inside a cylinder such that it touches the top, bottom, and the curved surface. Show that the volume of the sphere is two-thirds the volume of the cylinder.

• Prompt 3 (Problem Solve): From a solid wooden cylinder of height 20 cm and radius 14 cm, a cone of the same height and base is hollowed out. Find the volume of the remaining solid. Then, calculate the total surface area of the remaining solid.

• Prompt 4 (Synthesis): A metal cone of radius 12 cm and height 24 cm is melted and recast into spherical balls of radius 2 cm. Due to faulty processing, 10% of the metal is wasted. How many complete spherical balls can be made?

• Prompt 5 (Proof): The volume of a right circular cone is equal to the volume of a sphere. If the base radius of the cone is equal to the radius of the sphere, prove that the height of the cone is 4 times the radius.