Consider a cone with slant height 13 \text{ m} and perpendicular height 12 \text{ m}:
Find the length of the radius, r, of the base of this cone.
Hence, find the diameter of the base of the cone.
Consider the following triangular prism:
Find the exact length of CE.
Find the length of CX, correct to two decimal places.
Find the length of BE, correct to two decimal places.
The following solid is a right pyramid with a square base. The pyramid has its apex, V, aligned directly above the centre of its base, W.
Calculate the length of AW, correct to two decimal places.
Hence, find the length of VW, correct to two decimal places.
A soft drink can has a height of 11 cm and a radius of 4 cm. Find L, the length of the longest straw that can fit into the can.
Round your answer down to the nearest cm, to ensure it fits inside the can.
All edges of the given cube are 7 \text{ cm} long.
Find the exact length of EG as a surd.
Find the exact length of AG, in simplest surd form.
A square prism has dimensions of 12 cm by 12 cm by 15 cm as shown:
Calculate the length of HF, correct to two decimal places.
Calculate the length of DF, correct to two decimal places.
A rectangular prism has dimensions as shown:
Find the following in surd form:
The length of EG
The length of AG
The length of DG
The area of \triangle ADG
A juice container has the shape of a rectangular prism. It needs a straw that must extend 20 mm beyond the container while touching the furthest corner of the base.
Find the exact length of the diagonal of the base, x.
Hence, find the length of the long diagonal of the juice container, z. Round your answer to two decimal places.
Hence, calculate the length of the straw needed. Round your answer to the nearest millimetre.
A right-angled triangular divider has been placed inside a box, as shown in the diagram:
Calculate the area of the triangular divider, correct to two decimal places.
A builder needs to carry lengths of timber along a corridor in order to get them to where he is working. There is a right-angled bend in the corridor along the way. The corridor is 2 \text{ m} wide and the ceiling is 2.5 \text{ m} above the floor:
Calculate the maximum length of timber, in surd form, that would fit in the corridor when held parallel to the ground.
Since the corridor has a height of 2.5 \text{ m}, he can fit a longer piece of timber around the corner by angling it so that it reaches from the floor to the ceiling.
Find the maximum length of timber that is able to fit through the corridor, giving your answer correct to two decimal places.
A square prism has sides of length 3 \text{ cm}, 3 \text{ cm} and 14 \text{ cm} as shown:
Calculate the following to two decimal places:
z
\theta
In the figure is a right pyramid on a square base with its dimensions.
Calculate the following to two decimal places:
z
\theta
All edges of the following cube are 7 \text{ cm} long.
Find the length of the following edges as a simplified surd:
EG
AG
Find the measurement of the following angles, correct to two decimal places:
\angle EGH
\angle EGA
\angle AHG
\angle AGH
A rectangular prism has dimensions as shown:
Find the following lengths in surd form:
Find the area of \triangle ADG, in surd form.
Find the size of \angle DAG, correct to two decimal places.
A trianglular wedge has been inserted into the box as shown:
Find the size of angle x, correct to two decimal places.
A different trianglular wedge has been inserted into the box as shown:
Find the size of angle y, correct to two decimal places.
This following box is to have a divider placed inside it as shown:
If the diagonal AC has a length of z \text{ cm}, calculate the value of z to two decimal places.
Calculate the area of the divider, to two decimal places.
All edges of the base of the following square pyramid are 8 \text{ cm} long, while all the sloping edges are 12 \text{ cm} long:
Find the length of MD in surd form.
Find the size of \angle PDM, correct to two decimal places.
Find PM, the height of the pyramid, in surd form.
Find the length of MN.
Find the length of PN in surd form.
Find the size of \angle PNM, correct to two decimal places.
Find the size of \angle PDC, correct to two decimal places.
A cockroach starts at point B and crawls towards point C at 10 \text{ cm/min} on a 3.4 \text{ m} high ceiling. Sally is standing at a point A:
Calculate the distance in centimeters the cockroach will have crawled in the 3 minutes it take to reach point C.
The cockroach is now at point C. Calculate y, the distance in centimetres Sally will be from the point directly below the cockroach. Round your answer to two decimal places.
Calculate \theta, the angle of elevation from Sally to the cockroach at point C.