The diagram shows cuboid $$$A B C D E F G H$$$ of length $$$20 \mathrm{~cm}$$$ and width $$$5.5 \mathrm{~cm}$$$. The volume of the cuboid is $$$495 \mathrm{~cm}^{3}$$$. Find the angle between the line $$$A G$$$ and the base of the cuboid $$$A B C D$$$.

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_s20_qp_21 Year：2020 Question No：19

Answer:

$12.2$ or $12.24 \ldots$

Knowledge points:

E5.4.1 Carry out calculations involving the surface area and volume of a cuboid, prism and cylinder. (Answers may be asked for in multiples of π.)

E5.4.2 Carry out calculations involving the surface area and volume of a sphere, pyramid and cone. (Formulae will be given for the surface area and volume of the sphere, pyramid and cone in the question.)

E6.2.1 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right- angled triangle. (Angles will be quoted in degrees. Answers should be written in degrees and decimals to one decimal place.)

E6.2.2 Solve trigonometric problems in two dimensions involving angles of elevation and depression.

E6.2.3 Know that the perpendicular distance from a point to a line is the shortest distance to the line.

E6.5 Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.

The diagram shows cuboid $$\(A B C D E F G H\)$$ of length $$\(20 \mathrm{~cm}\)$$ and width $$\(5.5 \mathrm{~cm}\)$$. The volume of the cuboid is $$\(495 \mathrm{~cm}^{3}\)$$. Find the angle between the line $$\(A G\)$$ and the base of the cuboid $$\(A B C D\)$$.

Answer:

Knowledge points:

Solution:

The diagram shows cuboid $$\(A B C D E F G H\)$$ of length $$\(20 \mathrm{~cm}\)$$ and width $$\(5.5 \mathrm{~cm}\)$$. The volume of the cuboid is $$\(495 \mathrm{~cm}^{3}\)$$. Find the angle between the line $$\(A G\)$$ and the base of the cuboid $$\(A B C D\)$$.

Answer:

Knowledge points:

Solution:

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