Q. If the radius of a sphere is doubled, how does the volume change?
-
A.
It doubles
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B.
It triples
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C.
It quadruples
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D.
It increases by a factor of eight
Solution
Volume of a sphere = (4/3)πr³. If r is doubled, the new volume = (4/3)π(2r)³ = (4/3)π(8r³) = 8 times the original volume.
Correct Answer:
D
— It increases by a factor of eight
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Q. If two lines are parallel, what can be said about the alternate interior angles formed by a transversal?
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A.
They are equal
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B.
They are supplementary
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C.
They are complementary
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D.
They are unequal
Solution
When two parallel lines are cut by a transversal, the alternate interior angles are equal.
Correct Answer:
A
— They are equal
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Q. If two triangles have sides in the ratio 3:4:5, what can be said about their similarity?
-
A.
They are similar
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B.
They are congruent
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C.
They are not similar
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D.
Not enough information
Solution
Triangles with sides in the same ratio are similar.
Correct Answer:
A
— They are similar
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Q. In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, is triangle DEF a right triangle?
-
A.
Yes
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B.
No
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C.
Cannot be determined
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D.
Only if angle D is 90 degrees
Solution
Using the Pythagorean theorem: 8² + 6² = 64 + 36 = 100 = 10², so triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. What is the length of the diagonal of a rectangle with a length of 12 cm and a width of 9 cm?
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A.
15 cm
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B.
18 cm
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C.
21 cm
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D.
24 cm
Solution
Using the Pythagorean theorem: d² = length² + width² = 12² + 9² = 144 + 81 = 225, so d = 15 cm.
Correct Answer:
A
— 15 cm
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Q. What is the length of the diagonal of a rectangle with length 12 cm and width 9 cm?
-
A.
15 cm
-
B.
18 cm
-
C.
21 cm
-
D.
24 cm
Solution
Using the Pythagorean theorem: d² = length² + width² = 12² + 9² = 144 + 81 = 225, so d = 15 cm.
Correct Answer:
A
— 15 cm
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Q. What is the perimeter of a rectangle with a length of 10 cm and a width of 5 cm?
-
A.
30 cm
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B.
25 cm
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C.
20 cm
-
D.
15 cm
Solution
Perimeter = 2(length + width) = 2(10 + 5) = 30 cm.
Correct Answer:
A
— 30 cm
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