Area and Perimeter
- A wheel make 4000 revolution in moving a distance of 44 km. Find the radius of the wheel.
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Distance covered in 1 revolution
= (44 x 1000) / 4000
= 11 m
According to the question,
2πr = 11Correct Option: E
Distance covered in 1 revolution
= (44 x 1000) / 4000
= 11 m
According to the question,
2πr = 11
⇒ (44/7) x r = 11
∴ r = (11 x 7) / 44 = 1.75 m
- If the area of a semi-circle be 77 sq m, find its perimeter.
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According to the question,
Area of semi- circle = 77 m
(1/2) x π x r2 = 77
∴Circumference of semi- circle =πr + 2r
= ( π + 2)rCorrect Option: A
According to the question,
Area of semi- circle = 77 m
(1/2) x π x r2 = 77
⇒ r2 = (77 x 2 x 7)/22
∴ r = 7m
∴Circumference of semi- circle =πr + 2r
= ( π + 2)r
= [(22/7) + 2] x 7
= 36 m
- A railing of 288 m is required for fencing a semi-circular park. Find the area of the park. (π = 22/7)
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Let the radius of the park be r, then
πr + 2r = 288
Area of the park = (1/2)πr2Correct Option: A
Let the radius of the park be r, then
πr + 2r = 288
(π + 2)r = 288
⇒ [(22/7) + 2]r = 288
⇒ r = (288 x 7)/36 = 56
∴ Area of the park = (1/2)πr2
= (1/2) x (22/7) x 56 x 56
= 4928
- If the radius of a circle is increased by 6%, find the percentage increase in its area.
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Given that, a = 6
According to the formula,
Percentage increase in area
= 2a + [a2/100]%Correct Option: B
Given that, a = 6
According to the formula,
Percentage increase in area
= 2a + [a2/100]%
= 2 x 6 + [36/100]%
= (12 + 0.36)%
= 12.36%
- The wheel of an engine turns 350 times round its axle to cover a distance of 1.76 km. The diameter of the wheel is
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Distance covered in 1 round
= (Total Distance) / (Total round)Correct Option: D
Distance covered in 1 round
= (Total Distance) / (Total round)
= (1.76 x 1000)/350
= 176/35 m
∴ 2πr = (1.76 x 100) / 35 cm
2π = Diameter = 17600 x 7/22 x 35 = 160 cm