GCSE Secondary Maths Age 13-17 - Geometry & Measures: 3D Shapes - Volume - Explained

The video tutorial addresses a challenging geometry problem involving a container composed of a cylinder and a cone. The problem requires calculating the volume of both shapes and determining the height of the cylinder when the container is filled with grain at a constant rate. The tutorial emphasizes the importance of using π in calculations for non-calculator papers and provides a step-by-step solution to find the height H. The instructor highlights the complexity of the problem and offers advice on tackling similar questions.

What is the shape of the container described in the problem?

• A cone on top of a cylinder

• A cube on top of a cone

• A sphere on top of a cylinder

• A cylinder on top of a cone

Which formula is used to calculate the volume of a cone?

• π R-squared

• 2/3 π R-squared H

• 1/3 π R-squared H

• π R-squared H

Why is π used as a constant in the calculations?

• To avoid using decimals

• To make the problem more complex

• To follow the instructions on the formula sheet

• To simplify calculations in a non-calculator paper

After 5 hours, what is the total volume of grain filled in the container?

• 24π meters cubed

• 30π meters cubed

• 12π meters cubed

• 18π meters cubed

What is the rate of grain filling per hour?

• 8π meters cubed

• 7π meters cubed

• 6π meters cubed

• 5π meters cubed

What is the final calculated height of the cylinder?

• 42/9 meters

• 9/42 meters

• 14/3 meters

• 3/14 meters

What was the main challenge in solving this problem?

• Time constraints

• Inaccurate diagram

• Lack of formulas

• Complexity of calculations