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Stage 4 - Stage 5

Pythagoras in 3D

Interactive practice questions

Consider a cone with slant height $13$13m and perpendicular height $12$12m.

A cone with a circular base. The cone altitude, illustrated by a vertical dashed line, measures 12 meters, highlighted by a scale line on the left. The radius of the base circle is represented by a horizontal dashed line and is labeled r. These two lines are perpendicular, forming a right angle, which is denoted by a small square symbol. The slant height of the cone, which stretches from the apex to a point on the circumference of the base and opposite to the right angle, measures 13 meters, as indicated by the slanted scale line placed on the right. Together, the radius of the base (base), the altitude of the cone (height), and the slant height (hypotenuse) compose a right-angled triangle.


Find the length of the radius, $r$r, of the base of this cone.


Hence, find the length of the diameter of the cone's base.


A soft drink can has a height of $13$13 cm and a radius of $3$3 cm. Find $L$L, the length of the longest straw that can fit into the can (so that the straw is not bent and fits entirely inside the can).

Give your answer rounded down to the nearest cm, to ensure it fits inside the can.


A square prism has sides of length $11$11cm, $11$11cm and $15$15cm as shown.


A fruit juice container has the shape of a rectangular prism. It needs a straw that must extend $20$20 mm beyond the container while touching the furthest corner of the base.

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