Chapter 13 Class 10 Surface Areas and Volumes

Class 10
Important Questions for Exam - Class 10

### Transcript

Example 2 The decorative block shown in figure is made of two solids — a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block.(Take π = 22/7) Now, Total surface area of block = Total Surface area of cube + Curved Surface area of hemisphere – Base area of hemisphere Total Surface area of cube Given that side of cube is 5 cm Total Surface Area of the cube = 6 (side)2 = 6 (5)2 = 6 × 5 × 5 = 150 cm2 Curved surface area of hemisphere Diameter of hemisphere = 4.2 cm Radius = r = Diameter/2 = 4.2/2 = 2.1 cm Curved surface area of hemisphere = 2𝜋𝑟2 = 2 × 22/7 × (2.1)2 = 2 × 22/7 × 2.1 × 2.1 = 27.72 cm2 Base area of hemisphere Base of hemisphere is a circle with radius 2.1 cm Base area of hemisphere = Area of circle = 𝜋𝑟2 = 𝟐𝟐/𝟕×(𝟐.𝟏)𝟐 = 22/7×2.1×2.1 = 22×0.3×2.1 = 13.86 cm2 Therefore, Total surface area of block = Total Surface area of cube + Curved Surface area of hemisphere – Base area of hemisphere = 150 + 27.72 – 13.86 = 177.72 – 13.86 = 163.86 cm2

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.