Geometry MCQs for CCAT with Answers

Q1.

What is the area of a circle with radius 7 cm? (Use π = 22/7)

A154 cm²

B144 cm²

C164 cm²

D176 cm²

Show Answer & Explanation

Correct Answer: A - 154 cm²

Area = πr² = (22/7) × 49 = 154 cm².

Q2.

Find the perimeter of a rectangle with length 12 cm and breadth 8 cm.

A32 cm

B40 cm

C48 cm

D96 cm

Show Answer & Explanation

Correct Answer: B - 40 cm

Perimeter = 2(l+b) = 2(12+8) = 40 cm.

Q3.

The sum of angles of a triangle is:

A90°

B180°

C270°

D360°

Show Answer & Explanation

Correct Answer: B - 180°

The sum of interior angles of any triangle is 180°.

Q4.

Find the area of a triangle with base 10 cm and height 6 cm.

A20 cm²

B30 cm²

C40 cm²

D60 cm²

Show Answer & Explanation

Correct Answer: B - 30 cm²

Area = (1/2) × base × height = (1/2) × 10 × 6 = 30 cm².

Q5.

The diagonal of a square is 10√2 cm. Find its area.

A50 cm²

B100 cm²

C150 cm²

D200 cm²

Show Answer & Explanation

Correct Answer: B - 100 cm²

Diagonal = a√2, so a = 10. Area = a² = 100 cm².

Q6.

Find the circumference of a circle with diameter 14 cm.

A48 cm

B44 cm

C52 cm

D56 cm

Show Answer & Explanation

Correct Answer: B - 44 cm

Circumference = πd = (22/7) × 14 = 44 cm.

Q7.

In a right triangle, if two sides are 3 cm and 4 cm, find the hypotenuse.

A8 cm

B6 cm

C7 cm

D5 cm

Show Answer & Explanation

Correct Answer: D - 5 cm

Hypotenuse = √(3² + 4²) = √25 = 5 cm.

Q8.

The volume of a cube with side 5 cm is:

A100 cm³

B125 cm³

C150 cm³

D175 cm³

Show Answer & Explanation

Correct Answer: B - 125 cm³

Volume = side³ = 5³ = 125 cm³.

Q9.

Each interior angle of a regular hexagon is:

A108°

B135°

C120°

D144°

Show Answer & Explanation

Correct Answer: C - 120°

Interior angle = (n-2)×180/n = 4×180/6 = 120°.

Q10.

The surface area of a sphere with radius 7 cm is: (π = 22/7)

A576 cm²

B716 cm²

C686 cm²

D616 cm²

Show Answer & Explanation

Correct Answer: D - 616 cm²

Surface area = 4πr² = 4 × (22/7) × 49 = 616 cm².

Q11.

The area of a rhombus with diagonals 10 cm and 14 cm is:

A60 cm²

B80 cm²

C70 cm²

D140 cm²

Show Answer & Explanation

Correct Answer: C - 70 cm²

Area = (1/2) × d₁ × d₂ = (1/2) × 10 × 14 = 70 cm².

Q12.

The volume of a cone with radius 7 cm and height 12 cm is: (π = 22/7)

A528 cm³

B672 cm³

C616 cm³

D704 cm³

Show Answer & Explanation

Correct Answer: C - 616 cm³

Volume = (1/3)πr²h = (1/3) × (22/7) × 49 × 12 = 616 cm³.

Q13.

A cylinder has radius 7 cm and height 10 cm. Its curved surface area is: (π = 22/7)

A440 cm²

B420 cm²

C400 cm²

D460 cm²

Show Answer & Explanation

Correct Answer: A - 440 cm²

CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².

Q14.

Two parallel sides of a trapezium are 12 cm and 8 cm. If height is 5 cm, find area.

A40 cm²

B100 cm²

C60 cm²

D50 cm²

Show Answer & Explanation

Correct Answer: D - 50 cm²

Area = (1/2) × (a+b) × h = (1/2) × 20 × 5 = 50 cm².

Q15.

The angle subtended by a semicircle at any point on it is:

A45°

B90°

C60°

D180°

Show Answer & Explanation

Correct Answer: B - 90°

Angle in a semicircle is always 90° (theorem).

Q16.

If radius of a circle is increased by 50%, its area increases by:

A125%

B100%

C50%

D150%

Show Answer & Explanation

Correct Answer: A - 125%

New area = π(1.5r)² = 2.25πr². Increase = 125%.

Q17.

The perimeter of an equilateral triangle is 36 cm. Its area is:

A36√3 cm²

B27√3 cm²

C24√3 cm²

D18√3 cm²

Show Answer & Explanation

Correct Answer: A - 36√3 cm²

Side = 12 cm. Area = (√3/4) × 144 = 36√3 cm².

Q18.

A chord of length 16 cm is at distance 6 cm from center. Radius of circle is:

A8 cm

B12 cm

C10 cm

D14 cm

Show Answer & Explanation

Correct Answer: C - 10 cm

r² = 8² + 6² = 100. r = 10 cm.

Q19.

Volume of a hemisphere with radius 6 cm is: (π = 22/7)

A400 cm³

B428 cm³

C452.57 cm³

D350 cm³

Show Answer & Explanation

Correct Answer: C - 452.57 cm³

Volume = (2/3)πr³ = (2/3) × (22/7) × 216 = 452.57 cm³.

Q20.

The ratio of areas of two similar triangles is 9:16. Ratio of their sides is:

A81:256

B9:16

C3:4

D4:3

Show Answer & Explanation

Correct Answer: C - 3:4

For similar triangles, area ratio = (side ratio)². Side ratio = √(9/16) = 3:4.

Q21.

The area of a triangle with sides 3, 4, and 5 cm:

A8 cm²

B10 cm²

C12 cm²

D6 cm²

Show Answer & Explanation

Correct Answer: D - 6 cm²

3-4-5 is right triangle. Area=½×3×4=6 cm².

Q22.

If radius of a circle is 7 cm, its circumference is:

A44 cm

B42 cm

C48 cm

D36 cm

Show Answer & Explanation

Correct Answer: A - 44 cm

C=2πr=2×22/7×7=44 cm.

Q23.

The diagonal of a square with side 10 cm:

A20 cm

B10√2 cm

C10 cm

D5√2 cm

Show Answer & Explanation

Correct Answer: B - 10√2 cm

Diagonal=side×√2=10√2 cm.

Q24.

A triangle has angles in ratio 2:3:4. The largest angle is:

A100°

B90°

C60°

D80°

Show Answer & Explanation

Correct Answer: D - 80°

2x+3x+4x=180. 9x=180. x=20. Largest=80°.

Q25.

Area of a circle with diameter 14 cm:

A144 cm²

B154 cm²

C160 cm²

D176 cm²

Show Answer & Explanation

Correct Answer: B - 154 cm²

r=7. Area=πr²=22/7×49=154 cm².

Q26.

Volume of a cube with edge 5 cm:

A125 cm³

B150 cm³

C100 cm³

D75 cm³

Show Answer & Explanation

Correct Answer: A - 125 cm³

V=5³=125 cm³.

Q27.

The perimeter of a rectangle with length 12 cm and breadth 8 cm:

A40 cm

B36 cm

C48 cm

D32 cm

Show Answer & Explanation

Correct Answer: A - 40 cm

P=2(12+8)=40 cm.

Q28.

An equilateral triangle has side 6 cm. Its area:

A12√3 cm²

B9√3 cm²

C6√3 cm²

D18√3 cm²

Show Answer & Explanation

Correct Answer: B - 9√3 cm²

Area=(√3/4)×6²=(√3/4)×36=9√3 cm².

Q29.

Surface area of a sphere with radius 3 cm:

A36π cm²

B27π cm²

C12π cm²

D9π cm²

Show Answer & Explanation

Correct Answer: A - 36π cm²

SA=4πr²=4π×9=36π cm².

Q30.

If two supplementary angles are in ratio 2:3, the angles are:

A60° and 120°

B72° and 108°

C80° and 100°

D90° and 90°

Show Answer & Explanation

Correct Answer: B - 72° and 108°

2x+3x=180. x=36. Angles: 72° and 108°.

Q31.

Volume of a cylinder with radius 7 cm and height 10 cm:

A1500 cm³

B1440 cm³

C1386 cm³

D1540 cm³

Show Answer & Explanation

Correct Answer: D - 1540 cm³

V=πr²h=22/7×49×10=1540 cm³.

Q32.

The sum of interior angles of a hexagon:

A720°

B540°

C900°

D1080°

Show Answer & Explanation

Correct Answer: A - 720°

(6-2)×180=720°.

Q33.

If the diagonal of a rectangle is 13 cm and one side is 5 cm, the other side is:

A10 cm

B12 cm

C8 cm

D11 cm

Show Answer & Explanation

Correct Answer: B - 12 cm

Other side=√(13²-5²)=√(169-25)=√144=12 cm.

Q34.

Curved surface area of a cone with radius 5 cm and slant height 13 cm:

A65π cm²

B60π cm²

C50π cm²

D75π cm²

Show Answer & Explanation

Correct Answer: A - 65π cm²

CSA=πrl=π×5×13=65π cm².

Q35.

Two parallel lines cut by a transversal form co-interior angles. If one is 65°, the other is:

A65°

B115°

C125°

D55°

Show Answer & Explanation

Correct Answer: B - 115°

Co-interior angles are supplementary: 180-65=115°.

Q36.

Area of a trapezium with parallel sides 8 cm and 12 cm, and height 5 cm:

A50 cm²

B48 cm²

C60 cm²

D40 cm²

Show Answer & Explanation

Correct Answer: A - 50 cm²

Area=½×(8+12)×5=50 cm².

Q37.

If the circumference of a circle is 44 cm, its radius is:

A11 cm

B14 cm

C7 cm

D22 cm

Show Answer & Explanation

Correct Answer: C - 7 cm

2πr=44. r=44/(2×22/7)=7 cm.

Q38.

Volume of a hemisphere with radius 6 cm:

A108π cm³

B72π cm³

C144π cm³

D216π cm³

Show Answer & Explanation

Correct Answer: C - 144π cm³

V=2/3πr³=2/3×π×216=144π cm³.

Q39.

The angle subtended by an arc at the center is double the angle at the circumference. If center angle is 120°, circumference angle is:

A30°

B90°

C45°

D60°

Show Answer & Explanation

Correct Answer: D - 60°

Angle at circumference = 120/2 = 60°.

Q40.

A right circular cylinder has radius 4 cm. If its total surface area is 176π cm², height is:

A16 cm

B20 cm

C14 cm

D18 cm

Show Answer & Explanation

Correct Answer: D - 18 cm

TSA=2πr(r+h)=2π×4×(4+h)=176π. 8(4+h)=176. 4+h=22. h=18 cm.

Q41.

The length of an arc of a circle with radius 10 cm subtending 90° at center:

A20π cm

B10π cm

C15π cm

D5π cm

Show Answer & Explanation

Correct Answer: D - 5π cm

Arc=θ/360×2πr=90/360×2π×10=5π cm.

Q42.

If the perimeter of a square is 48 cm, its area is:

A156 cm²

B128 cm²

C144 cm²

D196 cm²

Show Answer & Explanation

Correct Answer: C - 144 cm²

Side=48/4=12. Area=144 cm².

Q43.

In a right triangle, if hypotenuse is 17 and one side is 8, the third side is:

A14

B12

C13

D15

Show Answer & Explanation

Correct Answer: D - 15

Third side=√(289-64)=√225=15.

Q44.

Volume of a cone with radius 3 cm and height 4 cm:

A12π cm³

B36π cm³

C9π cm³

D16π cm³

Show Answer & Explanation

Correct Answer: A - 12π cm³

V=1/3πr²h=1/3×π×9×4=12π cm³.

Q45.

Two circles with radii 5 and 3 cm. Distance between centers is 10 cm. Number of common tangents:

A2

B3

C4

D1

Show Answer & Explanation

Correct Answer: C - 4

The distance between centers is 10 cm, which is greater than the sum of the radii 5+3=8 cm. The circles are separate, so they have 4 common tangents.

Q46.

Area of a rhombus with diagonals 12 cm and 16 cm:

A48 cm²

B192 cm²

C96 cm²

D128 cm²

Show Answer & Explanation

Correct Answer: C - 96 cm²

Area=½×d1×d2=½×12×16=96 cm².

Q47.

The area of a sector with radius 14 cm and angle 45°:

A88 cm²

B44 cm²

C77 cm²

D66 cm²

Show Answer & Explanation

Correct Answer: C - 77 cm²

Area=θ/360×πr²=45/360×22/7×196=1/8×616=77 cm².

Q48.

If two triangles are similar and their sides are in ratio 2:3, ratio of their areas is:

A4:9

B2:3

C8:27

D6:9

Show Answer & Explanation

Correct Answer: A - 4:9

Ratio of areas = square of ratio of sides = 4:9.

Q49.

Lateral surface area of a cube with edge 8 cm:

A192 cm²

B384 cm²

C512 cm²

D256 cm²

Show Answer & Explanation

Correct Answer: D - 256 cm²

LSA=4×side²=4×64=256 cm².

Q50.

In a circle of radius 5 cm, a chord is 3 cm from center. Length of chord:

A8 cm

B6 cm

C10 cm

D4 cm

Show Answer & Explanation

Correct Answer: A - 8 cm

Half chord length = sqrt(5² - 3²) = sqrt(16) = 4 cm. Therefore full chord length = 8 cm.

Q51.

In a triangle, sides are 13, 14, and 15. Area is:

A72

B84

C90

D96

Show Answer & Explanation

Correct Answer: B - 84

Using Heron: s=21. Area=sqrt(21x8x7x6)=sqrt(7056)=84.

Q52.

A circle has radius 7 cm. Area of sector with angle 90 degrees is:

A38.5 sq cm

B44 sq cm

C49 sq cm

D154 sq cm

Show Answer & Explanation

Correct Answer: A - 38.5 sq cm

Sector area = 90/360 x pi x 7² = 49pi/4 = 38.5 using pi=22/7.

Q53.

The diagonal of a square is 10sqrt(2). Its area is:

A50

B100

C150

D200

Show Answer & Explanation

Correct Answer: B - 100

Diagonal=sqrt(2) side, so side=10 and area=100.

Q54.

If the radius of a sphere is doubled, volume becomes:

A2 times

B4 times

C6 times

D8 times

Show Answer & Explanation

Correct Answer: D - 8 times

Sphere volume is proportional to r³. Doubling radius multiplies volume by 8.

Q55.

A right triangle has hypotenuse 25 and one side 7. Other side is:

A18

B20

C22

D24

Show Answer & Explanation

Correct Answer: D - 24

Other side = sqrt(25² - 7²)=sqrt(625-49)=sqrt576=24.

Q56.

If two similar triangles have side ratio 3:5, their area ratio is:

A3:5

B6:10

C9:25

D27:125

Show Answer & Explanation

Correct Answer: C - 9:25

Areas of similar figures are proportional to squares of corresponding sides.

Q57.

The sum of interior angles of a polygon is 1260 degrees. Number of sides is:

A7

B8

C9

D10

Show Answer & Explanation

Correct Answer: C - 9

(n-2)180=1260 gives n-2=7, so n=9.

Q58.

A cylinder has radius 3 cm and height 10 cm. Curved surface area is:

A30pi

B45pi

C60pi

D90pi

Show Answer & Explanation

Correct Answer: C - 60pi

Curved surface area = 2pi rh = 2pi x 3 x 10 = 60pi.

Q59.

In a circle, angle subtended by a diameter at the circumference is:

A45 degrees

B60 degrees

C90 degrees

D180 degrees

Show Answer & Explanation

Correct Answer: C - 90 degrees

By Thales theorem, a diameter subtends a right angle at the circumference.

Q60.

The inradius of a right triangle with sides 6, 8, 10 is:

A1

B2

C3

D4

Show Answer & Explanation

Correct Answer: B - 2

For right triangle, inradius=(a+b-c)/2=(6+8-10)/2=2.

Geometry - Practice MCQs for CCAT

Geometry Question Bank for C-CAT

Geometry - Practice MCQs for CCAT

Geometry Question Bank for C-CAT

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