Confidence Builder Questions: SURFACE AREA of a SPHERE

Refer back to this example to build the Skills that Count.

RADIUS from the centre of the sphere to the edge (in any direction!)

The Formula:

Surface Area = 4πr²

When:

• π ≈ 3.14

• r = radius

  
  

Worked Example

A ball has a radius of 4 cm.

Find the surface area of the sphere.

Step 1

Write the formula.

Surface Area = 4πr²

Step 2

Change letters and symbols to numbers.

Surface Area =

4 × 3.14 × 4²

Step 3

Square the radius.

4² = 4 × 4 4² = 16

Step 4

Multiply.

Surface Area =

4 × 3.14 × 16 

Surface Area = 12.56 × 16   

Surface Area = 200.96

Step 5

Write the correct units.

Surface Area = 200.96 cm²

Confidence Builder Questions

Question 1:

A globe has a radius of 6 cm.

Find the surface area of the sphere.

Step 1

Write the formula.

Step 2

Change letters and symbols to numbers.

Step 3

Square the radius.

Step 4

Multiply.

Step 5

Write the correct units.

Question 2:

A large exercise ball has a radius of 9 cm.

Find the surface area of the sphere.

Step 1

Write the formula.

Step 2

Change letters and symbols to numbers.

Step 3

Square the radius.

Step 4

Multiply.

Step 5

Write the correct units.

Question 3: Over to you…

A spherical water tank has a radius of 5m.

Use the formula below to work out the surface area of the sphere.

Surface Area = 4πr²

The Skill that Counts

The tricky bit...

The RADIUS is HALF the DIAMETER of a circle.

The DIAMETER is double, or 2 times the RADIUS!

Many learners find that working through just one question like this is enough to start rebuilding confidence.

If you need Functional Skills Maths Level 2 for work progression but maths confidence is holding you back, Maths in a Month offers a £25 exam readiness review. This helps identify exactly which topics need attention so you can move forward with confidence.

Find out how you did below :)

Answer Sheet

Worked Example Answer

A ball has a radius of 4 cm.

Surface Area = 4πr² 

Surface Area = 4 × 3.14 × 4² 

Surface Area = 4 × 3.14 × 16 

Surface Area = 12.56 × 16 

Surface Area = 200.96 cm²

Question 1 Answer

A globe has a radius of 6 cm.

Surface Area = 4πr² 

Surface Area = 4 × 3.14 × 6² 

Surface Area = 4 × 3.14 × 36 

Surface Area = 12.56 × 36 

Surface Area = 452.16 cm²

Question 2 Answer

A large exercise ball has a radius of 9 cm.

Surface Area = 4πr² 

Surface Area = 4 × 3.14 × 9² 

Surface Area = 4 × 3.14 × 81 

Surface Area = 12.56 × 81 

Surface Area = 1017.36 cm²

Question 3 Answer

A spherical water tank has a radius of 5 m.

Surface Area = 4πr² 

Surface Area = 4 × 3.14 × 5² 

Surface Area = 4 × 3.14 × 25 

Surface Area = 12.56 × 25 

Surface Area = 314 m²