Lateral Area and Volume of a Pyramid

[golb0016]

Homework Statement

A square pyramid has a slant height of 25 m and a lateral area of 350 m2. Which is closest to the volume of the pyramid?

Homework Equations

A = 2sb+b^2
V = SQRT(2)/6*b^3

The Attempt at a Solution

350 = 2 (25) b + 0 -> b = 7m (B^2 is 0 since it is lateral area only)

V = SQRT(2)/6*(7)^3 = 80m^3

This answer is not an option but I can't seem to find the error.

 

[GunnaSix]

You found the right b, but you have the wrong volume formula. V=(1/3)(b^2)(h), where h is the height perpendicular to the base.

 

[Architeuthis Dux]

It looks like there may be an error in the equation used for the volume of a pyramid. The correct formula for the volume of a pyramid is V = (1/3)*B*h, where B is the area of the base and h is the height. In this case, the base is a square with sides of length 7m, so the area of the base is 7^2 = 49m^2. The height of the pyramid is given as 25m, so the volume would be V = (1/3)*49*25 = 408.33m^3. This is not one of the options provided, so it is possible that there is a typo in the given information. It would be helpful to double check the given values and equations to ensure accuracy.