यह page Chapter 6 के textbook numerical patterns—circumference, arc, sector, triangle/Heron, cyclic quadrilateral, circle/sector/segment और applications—को cover करता है।
Total: 16
Numerical 1
Circumference A circle has perimeter 44 cm. Find radius.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
C=2πr. 44=2×22/7×r, so r=7 cm.
Numerical 2
3 Significant Figures Find circumference for r=10 cm to 3 significant figures.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
C=2πr≈2×22/7×10=62.857...≈62.9 cm.
Numerical 3
Arc Length Find arc length for r=3.5 cm and θ=60°.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
l=2πr×60/360 = 22×1/6 = 11/3 ≈ 3.67 cm.
Numerical 4
Sector Perimeter Find perimeter of a sector with r=14 cm and θ=75°.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Arc=2πr×75/360≈18.33 cm. Add two radii: 18.33+28≈46.33 cm.
Numerical 5
Tyre Revolutions A tyre has diameter 56 cm. How far does it travel in one revolution?
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
C=πd=(22/7)×56=176 cm.
Numerical 6
Triangle Area An isosceles triangle has equal sides 15 cm and perimeter 40 cm. Find area.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Base=10 cm. Height=√(15²−5²)=10√2 cm. Area=½×10×10√2=50√2≈70.71 cm².
Numerical 7
Heron's Formula Find area of a triangle with sides 13 cm, 14 cm and 15 cm.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
s=21. Area=√(21×8×7×6)=84 cm².
Numerical 8
Rhombus Area A rhombus has diagonals 10 cm and 24 cm. Find its area.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Area=½d₁d₂=½×10×24=120 cm².
Numerical 9
Parallelogram Area Base=18 cm and perpendicular height=7 cm. Find area.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Area=bh=18×7=126 cm².
Numerical 10
Cyclic Quadrilateral A cyclic quadrilateral has sides 5, 5, 12, 12 cm. Find its area using Brahmagupta's formula.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
s=17. Area=√(12×12×5×5)=60 cm².
Numerical 11
Circle Area Find area of a circle with radius 7 cm.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Area=πr²=(22/7)×49=154 cm².
Numerical 12
Sector Area Find area of a 90° sector of radius 14 cm.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Area=π×14²×90/360 = 154 cm².
Numerical 13
Segment Area A 90° sector has radius 14 cm. Find the minor segment area.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Sector=154 cm²; triangle with two radii and included 90° has area 98 cm²; segment=56 cm².
Numerical 14
Scale Factor A square has side 5 cm. If every side is tripled, what is the new area?
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Old area=25 cm². New side=15 cm, new area=225 cm² = 9 times.
Numerical 15
Lane Stagger Adjacent circular lanes differ in radius by 1.22 m. Find extra distance around the two curved halves.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
Two semicircles make one full circle, so stagger=2π×1.22≈7.67 m.
Numerical 16
Inscribed Equilateral Triangle An equilateral triangle is inscribed in a circle of radius r. Find its area in terms of r.
Approach: Given values लिखें, सही formula चुनें और units check करें।
हिंदी में Step-by-Step Solution:
For an inscribed equilateral triangle, side=r√3. Area=(√3/4)(3r²)=3√3r²/4.