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Uttarakhand Board Class 10 Surface Areas and Volumes — practice questions

Explore 34 free Surface Areas and Volumes questions in Uttarakhand Board Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Surface Areas and Volumes questions and exercises with answers

Showing questions 1–30 of 34.

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 →A solid is composed of a cone and a hemisphere of equal radius. The ratio of the volumes of the cone (height equal to radius) to the hemisphere isRead the answer and worked solution →A pencil sharpened at one end represents a combination of two shapes:Read the answer and worked solution →Three solid metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere. The radius of the new sphere isRead the answer and worked solution →A medicine capsule is in the shape of a cylinder of length 14 mm and radius 2.5 mm with two hemispherical ends. The total surface area isRead the answer and worked solution →A solid wooden toy has 4 cm cube + 4 cm hemispherical depression. The volume of wood isRead the answer and worked solution →

Worked practice questions

The volume of a cube of side a is

  1. a cubed
  2. 6 a squared
  3. a squared
  4. 12 a
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Correct answer: A. a cubed

1. Volume = side × side × side. 2. = a × a × a. 3. = a cubed. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.2_

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The total surface area of a cube of side a is

  1. 4 a squared
  2. 6 a squared
  3. a cubed
  4. 12 a
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Correct answer: B. 6 a squared

1. A cube has 6 identical square faces. 2. Each face has area a squared. 3. Total surface area = 6 a squared. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.2_

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The volume of a sphere of radius r is

  1. 4 pi r squared
  2. (2/3) pi r cubed
  3. (4/3) pi r cubed
  4. (1/3) pi r cubed
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Correct answer: C. (4/3) pi r cubed

1. Standard formula for sphere volume. 2. V = (4/3) × pi × r cubed. 3. Hence option A. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.2_

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