CBSE Class 10 Math Question Paper 2018 | Q21A

Question 21A: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the given figure. If the height of the cylinder is 10 cm and its base is of radius 3. 5 cm. Find the total surface area of the article.

Video Explanation

Explanatory Answer | CBSE 2018 Maths Paper Q21A

The total surface area of the article = Curved surface area of cylinder + (2 × Curved surface area of hemisphere)

Step 1: Compute Curved Surface Area of Cylinder

Curved surface area of cylinder = 2πrh = 2 × \\frac{22}{7}) × \\frac{7}{2}) × 10
CSA of cylinder = 220 sq cm

Step 2: Compute Curved Surface Area of the 2 Hemispheres (Top and Bottom)

Radius of each hemisphere = 3.5 cm = \\frac{7}{2})cm
CSA of a hemisphere = 2πr² = 2 × \\frac{22}{7}) × \\frac{7}{2}) × \\frac{7}{2}) = 77 sq cm

Step 3: Compute Total Surface Area of the Object

∴ The total surface area of the article = 220 + (2 × 77) = 220 + 154 = 374 sq cm