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CBSE Class 10 Mensuration: Surface Areas & Volumes — practice questions — page 2

Explore 104 free Mensuration: Surface Areas & Volumes questions in CBSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Mensuration: Surface Areas & Volumes questions and exercises with answers

Showing questions 31–60 of 104.

A circle is inscribed in an equilateral triangle of side 12 cm. The area of the region between the triangle and the circle is approximatelyRead the answer and worked solution →A wire bent into a circle of radius 42 cm is now bent into a regular hexagon. The side of the hexagon isRead the answer and worked solution →The diameter of a wheel is 70 cm. The number of revolutions to go 11 km isRead the answer and worked solution →A circular field of radius 56 m has a path of width 7 m running around it. The area of the path isRead the answer and worked solution →Two concentric circles have areas in the ratio 1 : 4. The ratio of their radii isRead the answer and worked solution →A square is circumscribed about a circle of radius 7 cm. The area enclosed between the circle and the square isRead the answer and worked solution →A wheel of diameter 84 cm makes 75 revolutions. The distance covered isRead the answer and worked solution →A chord 16 cm long is drawn in a circle of radius 10 cm. The distance of the chord from the centre isRead the answer and worked solution →The volume of a cube of side a isRead the answer and worked solution →The total surface area of a cube of side a isRead the answer and worked solution →The volume of a sphere of radius r isRead the answer and worked solution →The volume of a right circular cylinder of radius r and height h isRead the answer and worked solution →The volume of a cone of radius r and height h isRead the answer and worked solution →The curved surface area of a sphere of radius r isRead the answer and worked solution →The volume of a hemisphere of radius 7 cm isRead the answer and worked solution →A cone of height 12 cm and radius 5 cm has volumeRead the answer and worked solution →A cylindrical tank has radius 7 m and height 10 m. Its volume isRead the answer and worked solution →The slant height of a cone of radius 6 cm and height 8 cm isRead the answer and worked solution →A cube of side 8 cm is melted and recast into 8 equal smaller cubes. The side of each smaller cube isRead the answer and worked solution →A sphere of radius 6 cm is melted and recast into a cone of radius 6 cm. The height of the cone isRead the answer and worked solution →A solid is in the shape of a cylinder of radius 7 cm and height 14 cm with a hemisphere of the same radius on top. The volume of the solid isRead the answer and worked solution →A frustum of a cone has radii 4 cm and 8 cm and height 3 cm. Its slant height isRead the answer and worked solution →The volume of a frustum of a cone with radii 6 cm and 3 cm and height 4 cm isRead the answer and worked solution →How many balls of radius 1 cm can be made from a solid sphere of radius 10 cmRead the answer and worked solution →A solid metallic cylinder of radius 6 cm and height 30 cm is melted and made into solid cubes of side 6 cm. The number of cubes isRead the answer and worked solution →A toy is in the shape of a cone surmounted on a hemisphere of the same radius 3.5 cm. The total height is 15.5 cm. The volume of the toy isRead the answer and worked solution →A spherical ball of iron of radius 6 cm is dropped into a cylinder of radius 12 cm partially full of water. The rise in water level isRead the answer and worked solution →A cylindrical glass tube of radius 1 cm is filled with water to depth 14 cm. A sphere of radius 1 cm is dropped in. The new water level rises byRead the answer and worked solution →The radii of two spheres are in the ratio 2 : 3. The ratio of their volumes isRead the answer and worked solution →A solid cylinder of radius r and height h is melted into a solid cone of the same radius r. The height of the cone isRead the answer and worked solution →

Worked practice questions

A circle is inscribed in an equilateral triangle of side 12 cm. The area of the region between the triangle and the circle is approximately

  1. 50 sq cm
  2. 15 sq cm
  3. 32 sq cm
  4. 25.04 sq cm
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Correct answer: D. 25.04 sq cm

1. Triangle area = (square root of 3)/4 × 144 ≈ 62.35 sq cm. 2. Incircle radius = side/(2 (square root of 3)) ≈ 3.464; area ≈ pi × 12 ≈ 37.71 (incircle). 3. Difference ≈ 62.35 - 37.71 ≈ 24.64 → option ≈ 25 sq cm. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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A wire bent into a circle of radius 42 cm is now bent into a regular hexagon. The side of the hexagon is

  1. 44 cm
  2. 22 cm
  3. 88 cm
  4. 14 cm
Show answer and solution

Correct answer: A. 44 cm

1. Wire length = 2 × (22/7) × 42 = 264 cm. 2. Hexagon perimeter = 6 × side = 264. 3. Side = 44 cm. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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The diameter of a wheel is 70 cm. The number of revolutions to go 11 km is

  1. 2500
  2. 5000
  3. 7500
  4. 10000
Show answer and solution

Correct answer: B. 5000

1. Circumference = pi × d = (22/7) × 70 = 220 cm = 2.2 m. 2. Revolutions = 11000 / 2.2. 3. = 5000. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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More Mathematics topics

Introduction to TrigonometryReal Numbers and PolynomialsArithmetic ProgressionStatistics and ProbabilityCoordinate GeometryLinear Equations in Two VariablesQuadratic EquationsTriangles and Circles