Question

Consider the square pyramid shown. If each dimension is doubled, how does the surface area change? The surface area doubles. The surface area triples. The surface area increases by 4 times. The surface area increases by 8 times.

Answer 1

The surface area increases by 4 times

Answer 2

Surface area of a square pyramid
A = b² + (2 * b * s)

Where,
b = Base length
s = Slant Height

Assume,
b = x
s = y

A = x² + (2 * x * y)
= x² + 2xy

If all dimensions are doubled
b = 2x
s = 2y

A = (2x)² + (2 * 2x * 2y)
A = 4x² + 8xy
A = 4 (x² + 2xy)

∴ The surface area increases by 4 times
The correct answer is the third choice