Introduction: This is a Measurement lesson focused on formulas and application. The key trick is to realize that many problems first require you to use Pythagoras' Theorem to find a missing length (like slant height or perpendicular height) before you can use the surface area formula.

The "S Pass" Foundation (නියත S එකකට)

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

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

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

• Prompt 4 (Calculate): Find the total surface area of a cone with radius 7 cm and slant height 10 cm. (Use π=722​).

• Prompt 5 (Calculate): Find the surface area of a sphere with radius 14 cm.

Climbing to a "C" (C එකට පාර)

• Prompt 1 (Problem Solve): A square-based pyramid has a base side of 10 cm and a perpendicular height of 12 cm. Find the slant height of a triangular face, and then find the total surface area.

• Prompt 2 (Problem Solve): A cone has a perpendicular height of 24 cm and a base radius of 7 cm. Find its total surface area.

• Prompt 3 (Problem Solve): The surface area of a sphere is 1386 cm². Find its radius.

• Prompt 4 (Problem Solve): Find the total surface area of a solid hemisphere of radius 7 cm.

• Prompt 5 (Application): A paper cone is made from a sector of a circle with radius 14 cm and angle 90°. Find the area of the curved surface of the cone.

Aiming for a "B" (B ඉලක්කය)

• Prompt 1 (Problem Solve): The slant edge of a square-based right pyramid is 13 cm and the base side is 10 cm. Find the perpendicular height of the pyramid and then find its total surface area.

• Prompt 2 (Problem Solve): The total surface area of a right circular cone is 704 cm². If its base radius is 7 cm, find its slant height and then its perpendicular height.

• Prompt 3 (Compare): Find the ratio of the surface area of a sphere to the total surface area of a solid hemisphere of the same radius.

• Prompt 4 (Application): A toy is formed by placing a cone on top of a hemisphere of the same radius. The radius is 3.5 cm and the total height of the toy is 15.5 cm. Find the total surface area of the toy.

• Prompt 5 (Working Backwards): The area of the canvas used for a conical tent (curved surface only) is 550 m². If the base radius is 7 m, find the perpendicular height of the tent.

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

• Prompt 1 (Challenge): A solid metal sphere of radius 10 cm is cut into two hemispheres. Calculate the percentage increase in the total surface area.

• Prompt 2 (Derive): A right circular cone just fits inside a cube of side 'a' such that the base of the cone is on one face of the cube and its apex touches the opposite face. Express the total surface area of the cone in terms of 'a' and π.

• Prompt 3 (Problem Solve): The height of a cone is equal to the radius of a sphere. The surface area of the sphere is equal to the total surface area of the cone. Prove that the radius of the cone's base is 3​ times its height.

• Prompt 4 (Synthesis): An empty ice cream cone (conical part) has a radius of 3 cm and a height of 4 cm. A scoop of ice cream (a perfect hemisphere) of radius 3 cm is placed on top. Find the total surface area of the ice cream and cone that is exposed to the air.

• Prompt 5 (Proof): The internal radius of a hemispherical bowl is 7 cm and the external radius is 7.7 cm. Find the total surface area of the bowl (inside, outside, and the rim).