Question

Find the volume and surface area of a pyramid with height $3\sqrt{2}cm$ and a square base with sides all 6 cm in length [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Volume $=\frac{1}{3}\times areaofbase\times h$

$=\frac{1}{3}\times (6\times 6)\times 3\sqrt{2}$

$=36\sqrt{2}c{m}^3$

$=50.91c{m}^3$

Surface Area = area of square + area of 4 triangles

We need slant height AC

$A{C}^2=3^2+(3\sqrt{2}{)}^2$ (By Pythagoras)

$A{C}^2=27$

$AC=\sqrt{27}$

$\therefore SA=areaofsquare+areaof4triangles=6\times 6+4(\frac{1}{2}\times 6\times \sqrt{27})$

$=98.35c{m}^2$