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

The video tutorial explains how to find the surface area of a quarter of a solid sphere, Shape S, given its volume. It details the process of calculating the radius using the volume formula and then finding the surface area by considering the curved part and two semicircles. The tutorial emphasizes the importance of showing all working steps for full marks and concludes with a discussion on the allocation of marks for each step.

What is the shape of the object being analyzed in the problem?

• A full sphere

• A quarter of a sphere

• A half sphere

• A cylinder

What is the formula used to find the volume of a sphere?

• 4/3 πr²

• 4/3 πr³

• 2/3 πr³

• πr²

How is the radius of the sphere determined from the given volume?

• By dividing the volume by π and taking the square root

• By multiplying the volume by 3/4 and taking the cube root

• By dividing the volume by 4/3 π and taking the cube root

• By multiplying the volume by π and taking the square root

What is the surface area of the two semicircles combined?

• 576π

• 288π

• 144π

• 72π

What is the total surface area of the quarter sphere before rounding?

• 904.778

• 576π

• 288π

• 144π

To how many significant figures should the final answer be rounded?

• Two

• Five

• Three

• Four

What is the final rounded surface area of the quarter sphere?

• 907 cm³

• 905 cm³

• 904 cm³

• 906 cm³