Question

The edges of the bases of the frustum of a regular square pyramid have lengths 5 and 9, and the slant height of the frustum is 6.

What is the volume of the frustrum


I will give 100 points

Answer 1

Given↷

• a ⇢5
• b ⇢9
• l ⇢6

To find ↷

• The volume of the frustum

Solution ↷

We know that,

`V = (1)/(3) (a{}^(2) + ab + b{}^(2))h \\`

Also,

`l {}^(2) = h {}^(2) + (b - a) {}^(2)`

`6{}^(2) = h {}^(2) + (9 - 5) {}^(2)`

`36 = h {}^(2) +16`

`h {}^(2) = 36 - 16`

`h = √(20)`

`h = 4.47`

Now , putting the value in the formula of volume

we get,

`V = (1)/(3) (5{}^(2)+ 5 * 9 + 9{}^(2))4.47 \\`

`V = (1)/(3) (25 + 5 * 9 + 81)4.47 \\`

`V = (1)/(3) (25 + 45 + 81)4.47 \\`

`V = (1)/(3) * 151 * 4.47 \\`

`V = 224.99`

Hence, the volume of the given frustum is 224.99 cubic unit