Question 34 (Choice 2) - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Transcript

Question 34 (Choice 2) There are two identical solid cubical boxes of side 7cm. From the top face of the first cube a hemisphere of diameter equal to the side of the cube is scooped out. This hemisphere is inverted and placed on the top of the second cube’s surface to form a dome. Find (i) the ratio of the total surface area of the two new solids formed (ii) volume of each new solid formed. Question 34 (Choice 2) – Part (i) Find (i) the ratio of the total surface area of the two new solids formed Solid I Here, Side of Cube = a = 7 cm Radius of Hemisphere = 7/2 cm Total Surface Area of Solid I = Total Area of cube + Curved surface area of hemisphere − Base area of hemisphere = 6a2 + 2𝜋r2 − 𝜋r2 = 6a2 + 𝜋r2 = 6 × 72 + 22/7×(7/2)^2 = 6 × 49 + 22/7×7/2 ×7/2 = 294 + 11 × 7/2 = 294 + 38.5 = 332.5 cm2 Solid II Total Surface Area of Solid II = Total Area of cube + Curved surface area of hemisphere − Base area of hemisphere = 6a2 + 2𝜋r2 − 𝜋r2 = 6a2 + 𝜋r2 = 6 × 72 + 22/7×(7/2)^2 = 6 × 49 + 22/7×7/2 ×7/2 = 294 + 11 × 7/2 = 294 + 38.5 = 332.5 cm2 Since Total Surface Area of both the Solids are 332.5 cm2 Therefore, Ratio of their Surface Area = 332.5 : 332.5 = 1 : 1Question 34 (Choice 2) – Part (ii) Find (ii) volume of each new solid formed.Now, Volume of Solid I = Volume of Cube − Volume of hemisphere And Volume of Solid II = Volume of Cube + Volume of hemisphere Volume of Cube Side of Cube = a = 7 cm Volume of cube = a3 = 73 = 7 × 7 × 7 = 343 cm3 Volume of Hemisphere Radius of Hemisphere = 7/2 cm Volume of Hemisphere = 2/3 𝜋𝑟^3 = 2/3 ×22/7 × (7/2)^3 = 2/3 ×22/7 ×7/2 ×7/2 × 7/2 7/2= 2/3 ×22/7 ×7/2 ×7/2 × 7/2 = 539/6 = 89.83 cm3 Thus, Volume of Solid I = Volume of Cube − Volume of hemisphere = 343 − 89.83 = 253.17 cm3 And Volume of Solid II = Volume of Cube + Volume of hemisphere = 343 + 89.83 = 432.83 cm3