Reema mother’s is making a table cover for round table. Reema painted a design on
it. It has six equal designs as shown in the given figure. The radius of the cover
A) Find ∟AOB
(i) 600
(ii) 700
(iii) 300
(iv) 650
B) Find area of ∆AOB
(i) 332 cm2
(ii) 322 cm2
(iii) 333 cm2
(iv) none of these
C) Find area of sector OAPB
(i) 1232
3
cm2
(ii)1322
3
cm2
(iii) 1223
3
cm2
(iv) 1223
5
cm2
D) Find area of a design.
(i) 411 cm2
(ii) 414 cm2
(iii) 465 cm2
(iv) 455 cm2
E) Find the cost of making the designs at the rate of Rs. 0.35 per cm2
(i) 160 (ii) 163 (iii) 164 (iv) 161
Answers
Complete Question :- Reema mother's is making a table cover for a round table. Reema painted a designe on it. It has six equal designs as shown in the given figure. The radius of the cover is 28 cm. find the cost of making the designs at the rate of Rs.0.35 per cm². ( use √3 = 1.73) .
Solution :-
→ ∠AOB = 360°/6 = 60°
Now, in ΔAOB we have,
→ OA = OB (Radius of the circle.)
→ ∠A = ∠B (Angle opposite to equal sides are equal.)
so,
→ ∠A + ∠B + ∠O = 180°
→ 2 ∠A = 180° - 60°
→ ∠A = 120°/2
→ ∠A = 60°
then,
∠A = ∠B = ∠C = 60°
therefore,
→ Area of Equilateral ΔAOB = (√3/4) * (OA)² = (√3/4) * (28)² = (√3 * 7 * 28) = 1.73 * 196 = 339.08 cm²
Also,
→ Area of sector AOB = (60°/360°) * π(radius)² = (1/6) * (22/7) * (28)² = (1/3) * 11 * 4 * 28 = (1232/3) = 410.67 cm².
Hence,
→ Area of design = Area of sector AOB - Area of equilateral ΔAOB = 410.67 - 339.08 = 71.59 cm².
So,
→ Area of 6 design = 6 * 71.59 = 429.54 cm².
∴
→ Total cost of making design = 429.54 * 0.35 = Rs.150.33 (Ans.)
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Answer:
(I)60°
(ii)none of these
(iii) 1232/3
(iv) ____
(v)