Surface Area Challenges
The cube has
volume 125cm3
The shaded circle
bisects the sphere.
Find its surface
area.
If the circle has area
49π cm2 find the
surface area of the
sphere.
BC = 6cm
Find the surface
area of the shaded
shape.
AC = 3√5 cm
AE = √13 cm
Find the surface
area of the shape.
Find the surface
area of the square
based pyramid
Find the surface
area of the hollow
tube.
A quarter of a
sphere is shown. If
the volume of this
shape is 9π cm3
what is its surface
area?
Find the surface
area of the squarebased pyramid.
Assuming face A has
rotational symmetry of
order 2, calculate the
surface area of the
whole 3-D shape.
The tip of the squarebased pyramid is
painted as shown,
2
using 40cm of paint.
The white area of the
triangular sides uses
2
210cm of paint
What is the width of
the base?
Answers
1. 𝟏𝟓𝟎𝒄𝒎𝟐
2. 𝟏𝟗𝟔𝝅𝒄𝒎𝟐 ≈ 𝟔𝟏𝟓. 𝟕𝟓𝒄𝒎𝟐
3. 𝟕𝟐𝒄𝒎𝟐
4. 𝟑𝟐𝟎𝝅/𝟗 + 𝟏𝟐𝟎 𝒄𝒎𝟐 ≈ 𝟐𝟑𝟏. 𝟕𝒄𝒎𝟐
5. 𝟕𝟐𝒄𝒎𝟐
6. 𝟓𝟎𝝅𝒄𝒎𝟐 ≈ 𝟏𝟓𝟕. 𝟏𝒄𝒎𝟐
7. 𝟏𝟖𝝅𝒄𝒎𝟐 ≈ 𝟓𝟔. 𝟓𝟓𝒄𝒎𝟐
8. 𝟏𝟔 + 𝟏𝟔𝒕𝒂𝒏 𝟕𝟎 𝒄𝒎𝟐 ≈ 𝟔𝟎. 𝟎𝒄𝒎𝟐 (𝟏𝒅𝒑)
9. 𝟐𝟒𝝅 + 𝟏𝟕𝟒 𝒄𝒎𝟐 ≈ 𝟐𝟒𝟗. 𝟑𝟗𝟖𝒄𝒎𝟐
10. 𝟏𝟐. 𝟓 𝒄𝒎