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Exam 6: Geometry

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Question 31

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Determine the value of angle $\theta$ .

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Question 32

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What will it cost to pave a driveway that is $22 \mathrm{~m}$ long and $4.8 \mathrm{~m}$ wide if the price is $\$ 0.15 / \mathrm{m}^{2}$ ?

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Question 33

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The hypotenuse of an isosceles right-angled triangle is $14.5 \mathrm{~cm}$ long. Determine the lengths of the other two sides.

Determine the value of angle $\theta$ .

An underground water main chamber has a concrete cover in the shape of a circle with a rectangle cut out for access. Calculate the cross-sectional area of the cover.

The height of a pyramid with a square base is $9.0 \mathrm{~cm}$ . The slant height makes an angle of $45^{\circ}$ with the pyramid base. Determine the volume of the pyramid.

A company in British Columbia manufactures spherical tree houses. One model has an outside diameter of $3.20 \mathrm{~m}$ and is made from made of fibreglass that is $3.00 \mathrm{~mm}$ thick. The fibreglass is lined on the inside with wood $18.0 \mathrm{~mm}$ thick. What is the volume of living space inside the sphere in $\mathrm{m}^{3}$ ?

A right prism with an equilateral triangle base of side length $25.0 \mathrm{dm}$ has a surface area of $1620 \mathrm{dm}^{2}$ . Determine the altitude of this prism.

What is the purchase cost, to the nearest dollar, of a triangular piece of land with base $40.0 \mathrm{~m}$ and altitude $64.0 \mathrm{~m}$ if the price is $\$ 0.65 / \mathrm{m}^{2}$ ?

A pyramid has four congruent triangular faces, each having a base of $23 \overline{0} \mathrm{~m}$ . The peak of the pyramid is $147 \mathrm{~m}$ above the base. How many litres of paint are needed to cover the pyramid if one litre of paint can cover $10.0 \mathrm{~m}^{2}$ .

Determine the lengths $A B$ and $B C$ , given that $A B \| M N$ .

A pyramid with a rectangular base measuring $2.45 \mathrm{~m}$ by $1.90 \mathrm{~m}$ is $2.10 \mathrm{~m}$ high at the peak. What is the volume?

A right prism has a base in the shape of a right isosceles triangle with hypotenuse measuring $8.5 \mathrm{~cm}$ . The height of the prism is $12 \mathrm{~cm}$ . (a) What is the volume? (b) What is the total surface area?

Determine the value of angle $\theta$ .

A bronze bushing in a right circular cylinder form has a height of $7.0 \mathrm{~cm}$ and a wall thickness of 0.90 $\mathrm{cm}$ . The outside diameter of the base is $5.0 \mathrm{~cm}$ . Determine the weight of $1 \mathrm{~cm}^{3}$ of bronze if the bushing weighs $0.68 \mathrm{~kg}$ .

Find angle $A$ in a triangle if the other two exterior angles are $107^{\circ}$ and $123^{\circ}$ .

Determine the values of angles $A, B$ , and $C$ .

What is the area of a circle with a circumference of $34 \mathrm{~m}$ ?

When a circle is removed from the centre of a larger circle, the area is halved. Determine the radius of the larger circle if the radius of the smaller circle is $1.414 \mathrm{~cm}$ .

A pair of tongs has handles that are $35.4 \mathrm{~cm}$ long and jaws that are $5.62 \mathrm{~cm}$ long. How far apart must the ends of the handles be to pick up a piece of hot metal that is $2.99 \mathrm{~cm}$ wide?