Ratio and proportion

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

A male punky fish has 9 stripes and a female punky fish has 8 stripes. I count 86 stripes on the fish in my tank. What is the ratio of male fish to female fish?

Can you fill in the mixed up numbers in this dilution calculation?

Malcolm and Nikki run at different speeds. They set off in opposite directions around a circular track. Where on the track will they meet?

Three-quarters of the junior members of a tennis club are boys and the rest are girls. What is the ratio of boys to girls among these members?