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Unit Test 6: Mensuration

Class 10 Mathematics (Standard)

Time: 1 Hour Max. Marks: 30

General Instructions:

  • The question paper consists of 15 questions divided into 4 sections: A, B, C, and D.
  • Section A: 6 MCQs of 1 mark each.
  • Section B: 4 Short Answer questions of 2 marks each.
  • Section C: 4 Short Answer questions of 3 marks each.
  • Section D: 1 Case Study based question of 4 marks.
  • Use of calculators is not permitted.
SECTION A (1 Mark Each)
[1] 1. Area of a sector of angle p (in degrees) of a circle with radius R is:
[1] 2. If the perimeter and the area of a circle are numerically equal, then the radius of the circle is:
[1] 3. A solid sphere of radius r is melted and recast into the shape of a solid cone of height r, the radius of the base of the cone is:
[1] 4. The surface area of a sphere is 616 cm². Its radius is:
[1] 5. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is:
[1] 6. The length of the minute hand of a clock is 14 cm. The area swept by the minute hand in 5 minutes is:
SECTION B (2 Marks Each)
[2] 7. Find the area of a quadrant of a circle whose circumference is 22 cm.
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[2] 8. Two cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.
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[2] 9. A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
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[2] 10. Find the area of the shaded region in a square ABCD of side 14 cm, where APD and BPC are semicircles.
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SECTION C (3 Marks Each)
[3] 11. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use π = 3.14)
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[3] 12. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
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[3] 13. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
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[3] 14. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc.
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SECTION D (Case Study - 4 Marks)
[4] 15. Case Study: Medicine Capsule

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm.

(i) Find the length of the cylindrical part. (1 Mark)
(ii) Find the surface area of the cylindrical part. (1 Mark)
(iii) Find the total surface area of the capsule. (2 Marks)
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TOTAL SCORE

0 / 6 (MCQ)

(Subjective answers submitted for review)

Solution Key (MCQs)

Q1. (d) (p/720) × 2πR²

Area = (p/360) × πR². Multiplying num and den by 2 gives (p/720) × 2πR².

Q2. (a) 2 units

2πr = πr² ⇒ 2r = r² ⇒ r = 2.

Q3. (b) 2r

Vol Sphere = Vol Cone ⇒ (4/3)πr³ = (1/3)πR²r ⇒ 4r² = R² ⇒ R = 2r.

Q4. (a) 7 cm

4πr² = 616 ⇒ 4(22/7)r² = 616 ⇒ r² = (616×7)/88 = 49 ⇒ r = 7.

Q5. (d) 16:9

Vol ratio 64:27 ⇒ r ratio 4:3 ⇒ Area ratio 16:9.

Q6. (c) 51.33 cm²

Angle = 30°. Area = (30/360) × (22/7) × 14 × 14 = 51.33 cm².