Geometry and Measures Practice Questions
GCSE · GCSE Mathematics · 129 free MCQs with instant results and detailed explanations.
129
Total
42
Easy
62
Medium
25
Hard
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Sample Questions from Geometry and Measures
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Q1
Easy
A triangle has angles measuring 50° and 60°. What is the measure of the third angle?
A.
70°
B.
60°
C.
80°
D.
90°
Show Answer & Explanation
Correct Answer: A
The sum of angles in a triangle is always 180°. Here, 50° + 60° + third angle = 180°. Therefore, the third angle = 180° - (50° + 60°) = 70°.
Q2
Easy
If a circle has a radius of 5 cm, what is its area?
A.
25π cm²
B.
10π cm²
C.
20π cm²
D.
15π cm²
Show Answer & Explanation
Correct Answer: A
The area of a circle is calculated using the formula Area = π * radius². Here, Area = π * (5 cm)² = π * 25 cm² = 25π cm².
Q3
Easy
What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?
A.
26 cm
B.
40 cm
C.
30 cm
D.
13 cm
Show Answer & Explanation
Correct Answer: A
The perimeter of a rectangle is calculated using the formula P = 2(length + width). Here, P = 2(8 cm + 5 cm) = 2(13 cm) = 26 cm.
Q4
Medium
A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What type of triangle is this?
A.
Right-angled triangle
B.
Equilateral triangle
C.
Isosceles triangle
D.
Scalene triangle
Show Answer & Explanation
Correct Answer: A
This triangle is a right-angled triangle because it satisfies the Pythagorean theorem: 7^2 + 24^2 = 25^2.
Q5
Medium
A circle has a radius of 10 cm. What is the area of the circle?
A.
100π cm²
B.
20π cm²
C.
50π cm²
D.
75π cm²
Show Answer & Explanation
Correct Answer: A
The area of a circle is given by the formula A = πr². Here, r = 10 cm, so A = π(10)² = 100π cm².
Q6
Medium
A cylinder has a radius of 4 cm and a height of 10 cm. What is the volume of the cylinder?
A.
160π cm³
B.
80π cm³
C.
40π cm³
D.
32π cm³
Show Answer & Explanation
Correct Answer: A
The volume of a cylinder is given by V = πr²h. Here, V = π(4)²(10) = 160π cm³.
Q7
Medium
A pyramid has a square base with a side length of 6 cm and a height of 9 cm. What is the volume of the pyramid?
A.
108 cm³
B.
72 cm³
C.
54 cm³
D.
36 cm³
Show Answer & Explanation
Correct Answer: A
The volume of a pyramid is given by V = (1/3) * base_area * height. Here, base_area = 6 cm * 6 cm = 36 cm², so V = (1/3) * 36 cm² * 9 cm = 108 cm³.
Q8
Hard
In a triangle, the lengths of two sides are 8 cm and 15 cm. What is the range of possible lengths for the third side?
A.
7 cm to 23 cm
B.
7 cm to 15 cm
C.
15 cm to 23 cm
D.
8 cm to 15 cm
Show Answer & Explanation
Correct Answer: A
According to the triangle inequality theorem, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, the length of the third side must be less than 8 cm + 15 cm = 23 cm and greater than the absolute difference of the two sides, which is |8 - 15| = 7 cm. Thus, the length of the third side can be between 7 cm and 23 cm.
Q9
Hard
A cylinder has a radius of 4 cm and a height of 10 cm. What is the total surface area of the cylinder? (Use π = 3.14)
A.
150.8 cm²
B.
200.8 cm²
C.
250.4 cm²
D.
314.0 cm²
Show Answer & Explanation
Correct Answer: A
The total surface area of a cylinder is calculated using the formula: Total Surface Area = 2πr(h + r). Plugging in the values: Total Surface Area = 2 * 3.14 * 4 * (10 + 4) = 2 * 3.14 * 4 * 14 = 150.8 cm². Therefore, the correct answer is 150.8 cm².
Q10
Hard
A triangle has sides measuring 7 cm, 24 cm, and 25 cm. What type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Right-angled
D.
Equilateral
Show Answer & Explanation
Correct Answer: C
This triangle is right-angled because it satisfies the Pythagorean theorem, where 7² + 24² = 25².
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Geometry and Measures — GCSE GCSE Mathematics Practice Questions Online
This page contains 129 practice MCQs for the chapter Geometry and Measures in GCSE GCSE Mathematics. The questions are organized by difficulty — 42 easy, 62 medium, 25 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.