by Gagan Pratap the area of a circular field. What will be the cost (in₹) of fencing the circular field at the rate of ₹35 per m? (Use 𝝅=𝟐𝟐𝟕 ) ,d vk;rkdkj ckx dh Hkqtk,a 176 m vkSj 56 m gSA bldk {ks=Qy ,d o`Rrkdkj eSnku ds {ks=Qy ds cjkcj gSA o`Rrkdkj eSnku esa #i;s 35 izfr m dh nj l ckM+ yxkus dh ykxr ¼#i;s esa½ fduh gksxh\ ¼ 𝝅=𝟐𝟐𝟕 dk mi;ksx dhft,½ 1.12,100 2.11,000 3.12,320 4.12,210 ( ICAR Technician 2023) 37. A wire is in the shape of a rectangle whose sides are in the ratio 4:3, and its area is 5808𝒄𝒎𝟐 . the same wire is bent to form a circle. What is the area (in 𝒄𝒎𝟐) of the circle? एक ताि एक आयत के आकाि का है जिसकी भुिाओं का अनुपात 4:3 है औि इसका क्षेत्रफल 5808𝒄𝒎𝟐 है। उसी ताि को एक वृत्त बनाने के ललए मोड़ा िाता है। वृत्त का क्षेत्रफल (𝒄𝒎𝟐 में) क्या है? A) 9856 B) 5544 C) 6545 D) 7546 38. A park is in a shape of a rectangle with length 180 m and breadth 120 m. At the centre of the park, there is a circular lawn of circumference 502.4m. The area of the park, excluding the area of lawn, in m² is: ,d vk;rkdkj ikdZ dh yackbZ 180 ehVj vkSj pkSM+kbZ 120 ehVj gSA ikdZ ds dsUæ 502.4 ehVj ifjf/k okyk ,d o`Ùkkdkj ykWu gSA ykWu ds {ks=Qy dks NksM+dj] ikdZ dk {ks=Qy m² esa fdruk gksxk\ (a)1540 (b)1405 (c)1504 (d)1450 39. In a circular field there is a rectangular tank of length 130m and 110m. If the area of land portion is 20350 m2 then find the radius of field? एक वृत्ताकाि मैिान में एक 130m × 110m माप वाला आयताकाि टैंक है। यदि शेष भाग का क्षेत्रफल 20350 m2 है तब मैिान की त्रत्रज्या होगी? a)96cm b)105cm c)122cm d)108cm 40. A rectangular sheet of length 42cm and breadth 14cm is cut from a circular sheet. What is the minimum area of circular sheet? एक वृताकाि शीट से एक आयताकाि शीट जिसकी लम्बाई 42cm औि चौड़ाई 14cm है काटा िाता है। तब वृताकाि शीट का न्यूनतम क्षेत्रफल क्या होगा? a)3080cm2 b)1540 cm2 c)770 cm2 d)1050 cm2 41. The perimeter of a semi-circle is 25.7 cm. What is its diameter (in cm)? ( = 3.14) fdlh v/kZo`Ùk dk ifjeki 25.7 cm gsA bldk O;kl ¼lseh- eas½ Kkr djasA ( = 3.14) (a)8 (b)12 (c)10 (d)9 42. The area (in cm²)of the semicircle whose radius is 15 cm is: (use 𝝅 = 3.14) एकइसेअर्धवृत्तकाक्षेत्रफल(सेमी² में)तजसकीतत्रज्या15 सेमीहै:(π = 3.14 काउियोगकरें) 1. 365.75 2. 357.25 3. 353.25 4. 361.75 ( ICAR Technician 2023)
Question
by Gagan Pratap the area of a circular field. What will be the cost (in₹) of fencing the circular field at the rate of ₹35 per m? (Use 𝝅=𝟐𝟐𝟕 ) ,d vk;rkdkj ckx dh Hkqtk,a 176 m vkSj 56 m gSA bldk {ks=Qy ,d oRrkdkj eSnku ds {ks=Qy ds cjkcj gSA oRrkdkj eSnku esa #i;s 35 izfr m dh nj l ckM+ yxkus dh ykxr ¼#i;s esa½ fduh gksxh\ ¼ 𝝅=𝟐𝟐𝟕 dk mi;ksx dhft,½ 1.12,100 2.11,000 3.12,320 4.12,210 ( ICAR Technician 2023) 37. A wire is in the shape of a rectangle whose sides are in the ratio 4:3, and its area is 5808𝒄𝒎𝟐 . the same wire is bent to form a circle. What is the area (in 𝒄𝒎𝟐) of the circle? एक ताि एक आयत के आकाि का है जिसकी भुिाओं का अनुपात 4:3 है औि इसका क्षेत्रफल 5808𝒄𝒎𝟐 है। उसी ताि को एक वृत्त बनाने के ललए मोड़ा िाता है। वृत्त का क्षेत्रफल (𝒄𝒎𝟐 में) क्या है? A) 9856 B) 5544 C) 6545 D) 7546 38. A park is in a shape of a rectangle with length 180 m and breadth 120 m. At the centre of the park, there is a circular lawn of circumference 502.4m. The area of the park, excluding the area of lawn, in m² is: ,d vk;rkdkj ikdZ dh yackbZ 180 ehVj vkSj pkSM+kbZ 120 ehVj gSA ikdZ ds dsUæ 502.4 ehVj ifjf/k okyk ,d oÙkkdkj ykWu gSA ykWu ds {ks=Qy dks NksM+dj] ikdZ dk {ks=Qy m² esa fdruk gksxk\ (a)1540 (b)1405 (c)1504 (d)1450 39. In a circular field there is a rectangular tank of length 130m and 110m. If the area of land portion is 20350 m2 then find the radius of field? एक वृत्ताकाि मैिान में एक 130m × 110m माप वाला आयताकाि टैंक है। यदि शेष भाग का क्षेत्रफल 20350 m2 है तब मैिान की त्रत्रज्या होगी? a)96cm b)105cm c)122cm d)108cm 40. A rectangular sheet of length 42cm and breadth 14cm is cut from a circular sheet. What is the minimum area of circular sheet? एक वृताकाि शीट से एक आयताकाि शीट जिसकी लम्बाई 42cm औि चौड़ाई 14cm है काटा िाता है। तब वृताकाि शीट का न्यूनतम क्षेत्रफल क्या होगा? a)3080cm2 b)1540 cm2 c)770 cm2 d)1050 cm2 41. The perimeter of a semi-circle is 25.7 cm. What is its diameter (in cm)? ( = 3.14) fdlh v/kZoÙk dk ifjeki 25.7 cm gsA bldk O;kl ¼lseh- eas½ Kkr djasA ( = 3.14) (a)8 (b)12 (c)10 (d)9 42. The area (in cm²)of the semicircle whose radius is 15 cm is: (use 𝝅 = 3.14) एकइसेअर्धवृत्तकाक्षेत्रफल(सेमी² में)तजसकीतत्रज्या15 सेमीहै:(π = 3.14 काउियोगकरें) 1. 365.75 2. 357.25 3. 353.25 4. 361.75 ( ICAR Technician 2023)
Solution
This text contains multiple questions, each of which requires a separate calculation. Here are the solutions for each:
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The area of the rectangle is given by the product of its sides. If the sides are in the ratio 4:3, let's denote the sides as 4x and 3x. Therefore, the area of the rectangle is 4x3x = 12x^2. Given that the area is 5808 cm^2, we can solve for x: 12x^2 = 5808, so x^2 = 484, and x = 22. Therefore, the sides of the rectangle are 88 cm and 66 cm. The perimeter of the rectangle is 2(88+66) = 308 cm. When the wire is bent into a circle, this becomes the circumference of the circle. The radius of the circle is the circumference divided by 2π, or 308 / (2*22/7) = 49 cm. Therefore, the area of the circle is πr^2 = 22/7 * 49^2 = 7546 cm^2. So, the answer is D) 7546.
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The area of the rectangular park is 180m * 120m = 21600 m^2. The radius of the circular lawn is the circumference divided by 2π, or 502.4 / (2*22/7) = 80m. Therefore, the area of the lawn is πr^2 = 22/7 * 80^2 = 20160 m^2. The area of the park excluding the lawn is the total area of the park minus the area of the lawn, or 21600 - 20160 = 1440 m^2. So, the answer is not in the options provided.
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The area of the rectangular tank is 130m * 110m = 14300 m^2. Given that the area of the land portion is 20350 m^2, the total area of the field is the sum of the area of the tank and the land portion, or 14300 + 20350 = 34650 m^2. The radius of the field is the square root of the total area divided by π, or sqrt(34650 / (22/7)) = 105m. So, the answer is b) 105cm.
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The area of the rectangular sheet is 42cm * 14cm = 588 cm^2. This is the minimum area of the circular sheet, since the rectangle was cut from it. So, the answer is not in the options provided.
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The perimeter of a semi-circle is given by πd + d, where d is the diameter. Given that the perimeter is 25.7 cm, we can solve for d: 25.7 = 3.14d + d, so d = 25.7 / (3.14 + 1) = 8 cm. So, the answer is a) 8.
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The area of a semi-circle is given by 1/2 * πr^2. Given that the radius is 15 cm, the area is 1/2 * 3.14 * 15^2 = 353.25 cm^2. So, the answer is 3. 353.25.
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