Question

22 The diagram shows a sphere of diameter xcm and a pyramid ABCDE with a horizontal
rectangular base BCDE.
Diagram NOT
accurately drawn
பாபாபாபாபா
5x cm
x cm
2xcm
с
x cm
The vertex A of the pyramid is vertically above the centre of the base so that
AB = AC = AD = AE.
BC = xcm, CD = 2x cm and AO = 5x cm.
The volume of the sphere is 288 cm
Calculate the total surface area of the pyramid.
Give your answer correct to the nearest cm?

Answer 1

Answer:

The vertex A of the pyramid is vertically above the centre of the base so that

AB = AC = AD = AE.

BC = x cm, CD = 2x cm and AO = 5x cm.

The volume of the sphere is 288 cm.

$v = \frac{1}{3} \times lwh \\ 288 = \frac{1}{3} \times x \times 2x \times 5x \\ \\ \frac{864}{10} = {x}^{3}$

$x = 4.42$

The total surface area of the pyramid,

$a = lw + l \sqrt{( { \frac{w}{2} )}^{2} + {h}^{2} } + w \sqrt{ { (\frac{l}{2} }^{2}) + {h}^{2} } \\ a =2 {x}^{2} + x \sqrt{( { \frac{2x}{2} )}^{2} + {5x}^{2} } + 2x \sqrt{ { (\frac{x}{2} }^{2}) + {5x}^{2} }$

$a =2 {x}^{2} + x \sqrt{6 {x}^{2} } + 2x \sqrt{ \frac{11}{2} {x}^{2} } \\ a =2 {x}^{2} + \sqrt{6} {x}^{2} + 2 {x}^{2} \sqrt{ \frac{11}{2} } \\ a = 9.14 {x}^{2} = 178.56 \: {cm}^{2}$

Answer 2

Answer:

Step-by-step explanation: