- The area of the removed semi-circular part with diameter PQ is given as 72π sq cm. The formula for the area of a semi-circle is (1/2) π r^2. - (1/2) π r^2 = 72π => r^2 = 144 => r = 12 cm. - The diameter PQ is 2 r = 2 12 = 24 cm. - The area of the rectangle PQRS is given as 768 sq cm. Area = length width = PQ PS. - 24 PS = 768 => PS = 768 / 24 = 32 cm. - The sides of the rectangle are PQ = RS = 24 cm and PS = QR = 32 cm. - When the semi-circle with diameter PQ is removed, the perimeter of the leftover portion consists of the three straight sides (PS, QR, RS) and the curved arc of the semi-circle along the diameter PQ. - Length of sides: PS = 32 cm, QR = 32 cm, RS = 24 cm. - Length of the semi- circular arc: This is half the circumference of a circle with radius r=12 cm. Circumference = 2 π r = 2 π 12 = 24π cm. Semi-circular arc length = (1/2) 24π = 12π cm. - Perimeter of the leftover portion = PS + QR + RS + Arc length = 32 + 32 + 24 + 12π. - Perimeter = 88 + 12π cm.
From a rectangle PQRS of area 768 sq cm, a semi-circular part with diameter PQ and area 72π sq cm is removed. Then what is the perimeter of the leftover portion?
Asked in GPSC Prelims CSP 1 2023 · Topic: General Concept (Maps, Scale, and Basic Cartographic Concepts)
More World and Physical Geography questions
- The ratio of length of each equal side to third side of an isosceles triangle is 5 : 6. If the area of the isosceles triangle is 108 sq. cm and the third side of the triangle is equal to the diameter of a circle, what will be the area of the circle (in sq. cm)?
- In fieldcraft, distance is underestimated when 1. the light is bright 2. the object is large in relation to its surroundings 3. there is compressed/low-lying ground between the observer and the object 4. looking uphill Select the correct answer using the code given below.
- The FIFA World Cup Football, 2022 will be hosted by
- The perimeter of a rhombus is 52 m and its shorter diagonal is 10 m. The length of the longer diagonal is
- How many medals have been won by India in the Tokyo Paralympics, 2021?
- Which one of the following forms of settlement develops around a lake ?
- K is facing South Direction. Then he turns right and walks for 20 m. After that he turns right and walks 10 m. Then he turns left and walks 10 m. Then he turns right and walks 20 m. Again he turns right and walks 60 m. In which direction he is from the starting point?
- If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192 cm². What is the area of the original rectangle ?