import math


def checkio(height, width):
    return [round(calculate_volume(height, width), 2), round(calculate_area(height, width), 2)]


def calculate_area(height, width):
    r_width = width / 2
    r_height = height / 2
    if r_width == r_height:
        return 4 * math.pi * math.pow(r_width, 2)
    return calculate_area_c_less_than_a(r_width, r_height) if height <= width else calculate_area_c_more_than_a(r_width, r_height)


def calculate_area_c_less_than_a(r_width, r_height):
    e = math.sqrt(1 - (math.pow(r_height, 2) / math.pow(r_width, 2)))
    return 2 * math.pi * math.pow(r_width, 2) + math.pi * (math.pow(r_height, 2) / e) * math.log((1 + e) / (1 - e))


def calculate_area_c_more_than_a(r_width, r_height):
    e = math.sqrt(1 - (math.pow(r_width, 2) / math.pow(r_height, 2)))
    return 2 * math.pi * math.pow(r_width, 2) * (1+(r_height/(r_width*e))*math.asin(e))


def calculate_volume(height, width):
    return (4 * math.pi / 3) * math.pow(width / 2, 2) * (height / 2)


# These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
    assert checkio(4, 2) == [8.38, 21.48], "Prolate spheroid"
    assert checkio(2, 2) == [4.19, 12.57], "Sphere"
    assert checkio(2, 4) == [16.76, 34.69], "Oblate spheroid"