The formula for the volume of a pyramid is:
V = (l * w * h) / 3
knowing the formula we can replace the letters with the values we know:
v = 162
h = 6
since they told us the pyramid is square, we know that both L and W would be the same, so now we CAN SAY L *W = L^2 and solve for that:
162 = (l^2 * 6) / 3
multiply both sides by 3
486 = l^2 * 6
divide both sides by 6:
81 = l^2
l = sqrt(81)
l = 9 feet
Refer to the attached image.
Let the height of the Empire State Building = BC = 'x'
John is standing at distance from Empire State Building = AB = 1 mile
The angle of elevation = 11°
In triangle ABC,
Consider 
x = 0.194 mile
Since 1 mile =5280 feet
So, x = 
= 1024.32 feet.
So, the height of the Empire State Building is 1024.32 feet.
THE ANSWER ABOVE IS INCORRECT!! If you are doing Apex, the answer is doubling a cube. It can't be done with a straightedge or compass so it is impossible and was believed to be Apollo wanted something of his doubled with was a cube.
Answer is D
After dilation the image remain same but it is stretched or shrinked to the original size.
That means the ratio of the sides and the angles between the sides remain same .
Here we did dilation of ABCD which made it to EFGH.
Hence the ratio of the corresponding sides of the original rectangle ABCD should remain same even after dilation.
the corresponding sides are : AB and EF
BC and FG
CD and GH
DA and HE
* Let us find ratio of the sides AB and BC
given that AB= 10 and BC= 14
AB/BC= 10/14 = 5 /7 ( 10 and 14 both are multiple of 2 so we reduced them by a factor of 2 )
* the raio of the corresponding sides EF and FG should be same ( 5/7)
in the option D EF= 25 and FG= 35
so EF/FG= 25/35 = 5 /7 ( both are multiple of 5 so we reduced them by the factor of 5 )
Since ratio of the corresponding sides are coming out to be same for the EFGH given in option D it should be the dilation of the ABCD
