11. Surface Area of 3D Shapes (Practice Questions)

Note:

Use Q1 and Q2 from Surface Area of 3D Shapes from GCSE.

The pyramid below is made up of a square base with side length of $6$ cm and $4$ identical triangles with height of $10$ cm.

Work out the surface area of the pyramid.

Answer: $156$ cm $^2$

Wrong Answers:

$216$ cm $^2$

$254$ cm $^2$

$96$ cm $^2$

WORKING:

Area of the square base of the pyramid = $6\times6 = 36$ cm $^2$ .

Area of each triangular base = $\dfrac{1}{2}\times10\times6=30$ cm $^2$ .

Surface area of pyramid = $36+(30\times4)=156$ cm $^2$ .

Calculate the surface area of the cylinder below to 2 decimal places.

Use $\pi=3.14$ .

Answer: $226.08$ cm $^2$

Wrong Answers:

$254.34$ cm $^2$

$110.52$ cm $^2$

$197.82$ cm $^2$

WORKING:

Net of the cylinder:

We can work out the length of the rectangle by calculating the circumference of the circle.

Circumference = $3.14\times2\times3=18.84$ cm.

Area of rectangle = $18.84\times9=169.56$ cm $^2$ .

Area of circle = $3.14\times3^2=28.26$ cm $^2$ .

Surface area of cylinder = $169.56+(28.26\times2)=226.08$ cm $^2$ .

Calculate the surface error of the shape shown above.

Answer: $396$ cm $^2$

Wrong Answers:

$380$ cm $^2$

$346$ cm $^2$

$426$ cm $^2$

WORKING:

The combined surface area of the front and back facing sides:

$2\times(7\times4+5\times2)=2\times(28+10)=76$ cm $^2$ .

Surface area of the bottom face:

$9\times10=90$ cm $^2$ .

Surface area of sides facing upwards:

$(4\times10)+[latex](5\times10)=40+50=90$ cm $^2$ .

Surface area of side facing left:

$7\times10=70$ cm $^2$ .

Surface area of side facing right:

$(2\times10)+(5\times10)=70$ cm $^2$ .

Total Surface area:

$76+90+90+70+70=396$ cm $^2$ .