Perimeter, area and volume - advanced

This lesson comprises two (2) master classes focusing on:

• Solving problems involving surface area
• Solving problems involving volume and capacity

Content:

MA5-ARE-P-01

Solve problems involving surface areas

• Identify the perpendicular heights and slant heights of right pyramids and right cones
• Apply Pythagoras’ theorem to find the slant heights, base lengths and perpendicular heights of right pyramids and right cones
• Solve problems involving the surface areas of right pyramids and compare methods of solution
• Apply the formula to find the curved surface area of right cones: \( A= \pi rl \), where \( r \) is the length of the radius and \( l \) is the slant height
• Apply the formula to find the surface area of spheres: \( A=4 \pi r^2 \), where \( r \) is the length of the radius
• Solve problems involving the surface area of solids in a variety of contexts including composite solids

MA5-VOL-P-01

Solve problems involving volumes

• Find the volume of right pyramids and right cones by using an appropriate formula: volume of pyramid or cone \( V= \frac{1}{3} Ah \), where \( A \) is the base area and \( h \) is the perpendicular height
• Find the volume of spheres by using an appropriate formula: volume of sphere \( V= \frac{4}{3} \pi r^3 \), where \( r \) is the length of the radius
• Apply knowledge of right pyramids, right cones and hemispheres to solve problems involving composite solids
• Solve practical problems related to the volumes and capacities of solids including right pyramids, right cones and spheres