Inside a square of side length 15 cm, another square is drawn by joining the midpoints of the sides. A circle is drawn inside the inner square so that all sides of this square are tangents to circle. If a solid hemisphere is made with radius same as that of circle, then what will be the total surface area of hemisphere (in square cm)? (Take π = 3.14)
Solution
Correct Answer: Option B
Side length of given square is 15 cm.
If midpoints of its sides are joined to form a square, the side length of this square will hypotenuse of triangle formed by halves of two adjacent sides of square and line segment formed by joining midpoint of these two sides.
⇒ Side length of inner square = √ (square of half of side length of original square + square of half of side length of original square) = √ (7.5 × 7.5 + 7.5 × 7.5) = 7.5√ 2 = 10.6 cm
Inside this inner square, a circle is formed so that all sides of square are tangents to circle. This is possible if side length of Inner Square equals diameter of circle formed.
⇒ Diameter of circle = 10.6 cm
⇒ Radius of circle = 10.6/2 cm = 5.3 cm
Total surface area of solid hemisphere = 3 × π × square of radius
Total surface area of solid hemisphere with radius 5.3 cm = 3 × 3.14 × 5.3 × 5.3 = 264.6 square cm
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