HKDSE (Hong Kong) · Mathematics Compulsory Part

Measures, Shape and Space

50 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 50 questions

A cylinder has base radius $6$ cm and height $15$ cm. Find its volume in cm $^{3}$ .
A cylinder has base radius $5$ cm and height $3$ cm. Find its volume in cm $^{3}$ .
A cone has base radius $6$ cm and height $12$ cm. Find its volume in cm $^{3}$ .
A cylinder has base radius $6$ cm and height $8$ cm. Find its volume in cm $^{3}$ .
A sphere has radius $9$ cm. Find its volume in cm $^{3}$ .
A cylinder has base radius $5$ cm and height $10$ cm. Find its volume in cm $^{3}$ .
A right-angled triangle has hypotenuse $26$ cm and one other side $10$ cm. Find the third side in cm.
A right-angled triangle has hypotenuse $75$ cm and one other side $21$ cm. Find the third side in cm.
In a right-angled triangle the two perpendicular sides are $15$ cm and $36$ cm. Find the length of the hypotenuse in cm.
A right-angled triangle has hypotenuse $164$ cm and one other side $36$ cm. Find the third side in cm.
In a right-angled triangle the two perpendicular sides are $21$ cm and $72$ cm. Find the length of the hypotenuse in cm.
In a right-angled triangle the two perpendicular sides are $36$ cm and $160$ cm. Find the length of the hypotenuse in cm.
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 4$ , $B C = 3$ and $A C = 5$ . Find $cos ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 12$ , $B C = 5$ and $A C = 13$ . Find $s in ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 15$ , $B C = 8$ and $A C = 17$ . Find $s in ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 12$ , $B C = 5$ and $A C = 13$ . Find $t an ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 4$ , $B C = 3$ and $A C = 5$ . Find $s in ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 15$ , $B C = 8$ and $A C = 17$ . Find $cos ∠ C$ .
A line with slope $2$ passes through $(2, 10)$ . Find its $y$ -intercept.
Find the distance between $P (0, 3)$ and $Q (3, 7)$ .
Find the midpoint of $A (- 3, - 8)$ and $B (- 5, 8)$ .
Find the distance between $P (- 4, 0)$ and $Q (1, 12)$ .
Find the slope of the line through $(- 1, 4)$ and $(1, 10)$ .
Find the midpoint of $A (- 4, - 5)$ and $B (2, 7)$ .
Find the distance between $P (- 4, 1)$ and $Q (4, 16)$ .
Find the slope of the line through $(0, - 3)$ and $(3, 3)$ .
A line with slope $- 3$ passes through $(2, - 4)$ . Find its $y$ -intercept.
Find the slope of the line through $(3, 1)$ and $(4, - 2)$ .
Find the size of one exterior angle of a regular polygon with 8 sides, in degrees.
Find the sum of the interior angles of a polygon with 20 sides, in degrees.
Find the sum of the interior angles of a polygon with 18 sides, in degrees.
Find the sum of the interior angles of a polygon with 5 sides, in degrees.
Find the size of one exterior angle of a regular polygon with 12 sides, in degrees.
Find the size of each interior angle of a regular polygon with 10 sides, in degrees.
A sector has radius $6$ cm and angle $9 0^{\circ}$ . Find its arc length in cm.
A sector has radius $6$ cm and angle $15 0^{\circ}$ . Find its arc length in cm.
A sector has radius $9$ cm and angle $9 0^{\circ}$ . Find its area in cm $^{2}$ .
A sector has radius $15$ cm and angle $9 0^{\circ}$ . Find its area in cm $^{2}$ .
A sector has radius $18$ cm and angle $15 0^{\circ}$ . Find its arc length in cm.
Two similar solids have corresponding lengths in the ratio $2 : 5$ . The smaller solid has volume $8$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Two similar figures have corresponding lengths in the ratio $2 : 3$ . The smaller figure has area $12$ cm $^{2}$ . Find the area of the larger figure in cm $^{2}$ .
Two similar solids have corresponding lengths in the ratio $2 : 5$ . The smaller solid has volume $24$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Two similar solids have corresponding lengths in the ratio $4 : 5$ . The smaller solid has volume $128$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Two similar solids have corresponding lengths in the ratio $2 : 3$ . The smaller solid has volume $16$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Find the area of a circle with diameter $6$ cm, in cm $^{2}$ .
A chord of length $10$ cm lies $12$ cm from the centre of a circle. Find the radius in cm.
Find the area of a circle with diameter $24$ cm, in cm $^{2}$ .
A chord of length $12$ cm lies $8$ cm from the centre of a circle. Find the radius in cm.
A circle has area $25 π$ cm $^{2}$ . Find its circumference in cm.
Find the area of a circle with diameter $12$ cm, in cm $^{2}$ .

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