Question

45 POINTS FOR SOLVING THIS!!

Answer 1

Surface area of the pyramid = 157.99 in²

Explanation:

Volume of a pyramid is given by the formula,

Volume =
`(1)/(3)(\text{Area of the base})* \text{height}`

100 =
`(1)/(3)\text{(Side)}^(2) * \text{height}`

300 = s² × 5

s² = 60

s = √60

s = 2√15 in ≈ 7.746 in

Now surface area of the pyramid = Area of base + 4×(Area of one lateral side)

Area of square base = (Side)² = 60 in

Area of one lateral side =
`(1)/(2)(\text{Base})(\text{Lateral height})`

Since Lateral height =
`\sqrt{(h)^(2)+((S)/(2))^(2)}` [By applying Pythagoras theorem in the given triangle]

=
`\sqrt{(5)^(2)+(3.873)^(2)}`

=
`√(25+15)`

=
`√(40)`

= 6.325 in.

Now area of lateral side =
`(1)/(2)(7.746)(6.325)`

= 24.497 in²

Surface area of the pyramid = 60 + (4×24.497)

= 60 + 97.987

= 157.987 in²

≈ 157.99 in²

Answer 2

157.98
`in^2`

Explanation:

Given: volume of pyramid is equal to 100 cubic inches and height of the pyramid is 5 inches

To find: surface area of the pyramid

Solution:

Let h denotes the height of the pyramid and 'a' denotes side of the square base of the pyramid.

Volume of the pyramid =
`(1)/(3)a^2h`

Also,

Volume of the pyramid = 100 cubic inches

`(1)/(3)a^2h=100\\(1)/(3)a^2(5)=100\\a^2=(100* 3)/(5)=60\\a=√(60)`

Surface area of the pyramid
`(S) =a√(4h^2+a^2)+a^2`

So,

`S=√(60)√(100+60)+60\\=√(60)√(160)+60\\=√(9600)+60\\=97.9796+60\\=157.9796\\\approx 157.98`

Surface area = 157.98
`in^2`