Kuwait University Aptitude Tests (KUAT) · Mathematics and Quantitative Reasoning

Measures, Shape and Space

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

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A cone has base radius $9$ cm and height $15$ cm. Find its volume in cm $^{3}$ .
A cone has base radius $9$ cm and height $12$ cm. Find its volume in cm $^{3}$ .
A cone has base radius $6$ cm and height $3$ cm. Find its volume in cm $^{3}$ .
A sphere has radius $12$ cm. Find its volume in cm $^{3}$ .
A cylinder has base radius $8$ cm and height $10$ cm. Find its volume in cm $^{3}$ .
A cylinder has base radius $3$ cm and height $4$ cm. Find its volume in cm $^{3}$ .
A right-angled triangle has hypotenuse $5$ cm and one other side $3$ cm. Find the third side in cm.
In a right-angled triangle the two perpendicular sides are $40$ cm and $42$ cm. Find the length of the hypotenuse in cm.
In a right-angled triangle the two perpendicular sides are $8$ cm and $15$ cm. Find the length of the hypotenuse in cm.
A right-angled triangle has hypotenuse $17$ cm and one other side $8$ cm. Find the third side in cm.
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 24$ , $B C = 7$ and $A C = 25$ . Find $cos ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 12$ , $B C = 5$ and $A C = 13$ . Find $cos ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 24$ , $B C = 7$ and $A C = 25$ . Find $t an ∠ C$ .
In triangle $A B C$ , $∠ B = 9 0^{\circ}$ , $A B = 15$ , $B C = 8$ and $A C = 17$ . Find $t an ∠ C$ .
Find the distance between $P (4, 0)$ and $Q (7, 4)$ .
Find the slope of the line through $(3, - 3)$ and $(7, 5)$ .
Find the distance between $P (5, 3)$ and $Q (10, 15)$ .
Find the distance between $P (- 3, - 1)$ and $Q (2, 11)$ .
Find the slope of the line through $(- 3, 2)$ and $(- 2, 0)$ .
Find the slope of the line through $(1, 3)$ and $(3, 11)$ .
Find the distance between $P (- 3, - 2)$ and $Q (5, 13)$ .
Find the sum of the interior angles of a polygon with 12 sides, in degrees.
Find the size of each interior angle of a regular polygon with 5 sides, in degrees.
A sector has radius $6$ cm and angle $6 0^{\circ}$ . Find its area in cm $^{2}$ .
A sector has radius $15$ cm and angle $7 2^{\circ}$ . Find its arc length in cm.
A sector has radius $12$ cm and angle $12 0^{\circ}$ . Find its arc length in cm.
Two similar solids have corresponding lengths in the ratio $3 : 5$ . The smaller solid has volume $54$ cm $^{3}$ . Find the volume of the larger solid in cm $^{3}$ .
Two similar figures have corresponding lengths in the ratio $2 : 5$ . The smaller figure has area $20$ cm $^{2}$ . Find the area of the larger figure in cm $^{2}$ .
A chord of length $20$ cm lies $24$ cm from the centre of a circle. Find the radius in cm.
A circle has area $9 π$ cm $^{2}$ . Find its circumference in cm.
A circle has area $64 π$ cm $^{2}$ . Find its circumference in cm.
Find the area of a circle with diameter $20$ cm, in cm $^{2}$ .

Measures, Shape and Space

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