NZ Level 6 (NZC) Level 1 (NCEA)
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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
Approx 2 minutes
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A soft drink can has a height of $11$11cm and a radius of $4$4cm. 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.

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

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