GCSE Secondary Maths Age 13-17 - Geometry & Measures: Volume - Cone and Hemisphere - Explained

The video tutorial explains how to calculate the volume of a solid composed of a hemisphere and a cone. It guides through understanding the problem, using the correct formulae, and performing calculations accurately. The tutorial emphasizes the importance of not rounding off intermediate results and provides tips for ensuring accuracy in mathematical computations.

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

• A cube and a pyramid

• A cylinder and a cone

• A hemisphere and a cone

• A cylinder and a sphere

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

• 1/2 π r² h

• π r² h

• 1/3 π r² h

• 4/3 π r³

What is the formula for the volume of a sphere?

• 1/3 π r² h

• 2/3 π r³

• 4/3 π r³

• π r² h

How is the height of the cone determined in this problem?

• By using the total height of the solid

• By adding the radius of the hemisphere to the total height

• By using the diameter of the hemisphere

• By subtracting the radius of the hemisphere from the total height

What is the calculated volume of the cone before rounding?

• 134.041286553

• 167.55160819

• 301.592894743

• 302

What is the final volume of the solid, rounded to three significant figures?

• 303 cm³

• 302 cm³

• 301 cm³

• 300 cm³

What is a key tip for avoiding errors in calculations?

• Estimate the values instead of calculating

• Use the pi button on your calculator and avoid early rounding

• Use a different formula for each calculation

• Round off each intermediate result