Geometry question and answers

ARITHMETIC : GEOMETRY 

Geometry questions with solution for Railways NTPC, ALP , JE and SSC..

Most expected multiple choice question ❓ and answers with explanation.

1. In the given figure, ∠BAC = 90°, and AD is perpendicular to BC. Find the number of right triangles in the given figure.

A. 90°.            B. 180°.         C. 60°.        D. 120 °

2. Find the missing angle in the given figure.

A. 60°.          B. 75°.           C. 50°.        D. 35°

3. Find the curved surface area of a hemisphere whose radius is 14 cm.

A. 1232 cm².     B. 1122 cm².   C. 2211 cm².   D. 1233 cm²

4. The base area of a cylinder is 154 cm² and height is 5 cm. Find the volume of a cylinder.

A. 750 cm².        B. 770 cm².         C. 780 cm².        D. 700 cm²

5. Find the volume of a cone in terms π, whose radius is 3 cm and height is 4 cm.

A. 13 π cm³.         B. 12 π cm³.         C. 14 π cm³ D. 16 π cm³.

Solutions :- 

1. A

Given: ∠BAC = 90° and AD⊥BC.

Since AD⊥BC, the two possible right triangles obtained are ∠ADB and ∠ADC.

Hence, the number of right triangles in the given figure is 3.

I.e., ∠BAC = ∠ADB = ∠ADC = 90°.

2. C

Given two angles are 35° and 95°.

Let the unknown angle be “x”.

We know that sum of angles of a triangle is 180°

Therefore, 35°+95°+x = 180°

130°+ x = 180°

x = 180° – 130°

x = 50°

Hence, the missing angle is 50°.

3. A

Given: Radius = 14 cm.

As we know, the curved surface area of a hemisphere is 2πr² square units.

CSA of hemisphere = 2×(22/7)×14×14

CSA = 2×22×2×14

CSA = 1232

Hence, the curved surface area of a hemisphere is 1232 cm².

4. B

Given: Base area of a cylinder = 154 cm².

As the base area of a cylinder is a circle, we can write πr²= 154cm²

We know that the volume of a cylinder is πr²h cubic units.

V = 154(5) cm³

V = 770 cm³

Hence, the volume of a cylinder is 770 cm².

5. B

Given: Radius = 3 cm

Height = 4 cm

We know that the formula to find the volume of a cone is V = (⅓)πr²h cubic units.

Now, substitute the values in the formula, we get

V = (⅓)π(3)2(4)

V = π(3)(4)

V = 12 π cm³

Hence, the volume of a cone in terms of π is 12 π cm³.

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