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

Explore 73 free Mensuration: Surface Areas & Volumes questions in UP Board 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 73.

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 →A bucket in the shape of a frustum has radii 22 cm and 12 cm and height 24 cm. The slant height isRead the answer and worked solution →The volume of a frustum of a cone with radii 7 cm and 14 cm and height 12 cm isRead the answer and worked solution →A sphere of radius r is inscribed in a cube. The ratio of the volume of the sphere to the volume of the cube isRead the answer and worked solution →

Worked practice questions

A circular field of radius 56 m has a path of width 7 m running around it. The area of the path is

  1. 3000 sq m
  2. 2200 sq m
  3. 2618 sq m
  4. 1500 sq m
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Correct answer: C. 2618 sq m

1. Outer radius = 56 + 7 = 63 m; outer area = (22/7) × 63 × 63 = 12474 sq m. 2. Inner area = (22/7) × 56 × 56 = 9856 sq m. 3. Path area = 12474 - 9856 = 2618 sq m. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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Two concentric circles have areas in the ratio 1 : 4. The ratio of their radii is

  1. 2 : 1
  2. 1 : 4
  3. 1 : 8
  4. 1 : 2
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Correct answer: D. 1 : 2

1. Area ratio = (r1/r2) squared = 1/4. 2. Square root: r1/r2 = 1/2. 3. Hence 1 : 2. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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A square is circumscribed about a circle of radius 7 cm. The area enclosed between the circle and the square is

  1. 42 sq cm
  2. 77 sq cm
  3. 154 sq cm
  4. 196 sq cm
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Correct answer: A. 42 sq cm

1. Square side = 2 × 7 = 14 cm; square area = 196 sq cm. 2. Circle area = (22/7) × 49 = 154 sq cm. 3. Difference = 196 - 154 = 42 sq cm. _Source: syllabus Mathematics, Ch 11 "Areas Related to Circles", §11.2_

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More Mathematics topics

Arithmetic ProgressionReal Numbers and PolynomialsStatistics and ProbabilityIntroduction to TrigonometryAlgebra: Simultaneous Linear Equations & QuadraticsTriangles and CirclesCoordinate GeometryQuadratic Equations