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Bihar Board Class 10 (BSEB) Surface Areas and Volumes — practice questions

Explore 34 free Surface Areas and Volumes questions in Bihar Board Class 10 (BSEB) 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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