New Zealand
Level 6 - NCEA Level 1

# Pythagoras in 3D

## Interactive practice questions

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

a

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

b

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

Easy
1min

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.

Easy
2min

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

Easy
4min

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.

Easy
5min

### Outcomes

#### GM6-6

Use trigonometric ratios and Pythagoras’ theorem in two and three dimensions

#### 91031

Apply geometric reasoning in solving problems

#### 91032

Apply right-angled triangles in solving measurement problems