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UP Board Class 10 Mensuration: Surface Areas & Volumes — practice questions — page 3

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 61–73 of 73.

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 →A cylindrical bucket of height 14 cm and base radius 7 cm is full of water and is poured into a rectangular tank of base 22 cm × 14 cm. The height of water in the tank isRead the answer and worked solution →A hollow cylindrical pipe has outer radius 4 cm, inner radius 3 cm and height 10 cm. The volume of the material isRead the answer and worked solution →Match each part of a circleRead the answer and worked solution →Key in the circle answerRead the answer and worked solution →Sector or segment?Read the answer and worked solution →True or false: circles and sectorsRead the answer and worked solution →Match each solid to its shapeRead the answer and worked solution →True or false: solidsRead the answer and worked solution →

Worked practice questions

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 is

  1. 1 : 1
  2. 1 : 2
  3. 2 : 1
  4. 1 : 3
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Correct answer: B. 1 : 2

1. Cone volume = (1/3) pi r squared × r = (1/3) pi r cubed. 2. Hemisphere volume = (2/3) pi r cubed. 3. Ratio = (1/3) : (2/3) = 1 : 2. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.3_

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A pencil sharpened at one end represents a combination of two shapes:

  1. Two cylinders
  2. Cylinder and sphere
  3. Cylinder and cone
  4. Cone and cone
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Correct answer: C. Cylinder and cone

1. Pencil body is a long cylindrical shape. 2. Sharpened tip tapers to a point — that is a cone. 3. Combination: cylinder + cone. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.3_

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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 is

  1. 10 cm
  2. 9 cm
  3. 14 cm
  4. 12 cm
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Correct answer: D. 12 cm

1. Sum of volumes: (4/3) pi (216 + 512 + 1000) = (4/3) pi × 1728. 2. New sphere radius cubed = 1728, so radius = 12 cm. 3. Hence 12 cm. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.3_

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