the area of two equal circles in the figure is 308 cm. find the area of the rectangle
Answers
Answer:
area of rectangle = 98 cm²
Step-by-step explanation:
Area of two equal circles is 2 x πr²
=> 2 x 22/7 x r x r = 308
=> r² = 308/2 x 7/22
=> r² = 49
=> r = √49
= 7 cm
Now,
2r = diameter of circle = length of rectangle length=14 cm
radius of circle = breadth of rectangle=7 cm
therefore,
area of rectangle = length× breadth
= 14 × 7
= 98 cm²
area of rectangle = 98cm²
\sf\huge\underline{Answer :-}
Answer:−
Given :
Area of two equal circles = 308 cm²
To find :
Area of the rectangle
Solution :
\sf Area \: of \: two \: circles \: = \: 308 \: {cm}^{2}Areaoftwocircles=308cm
2
\sf \therefore Area \: of \: one \: circle \: \rightarrow \dfrac{308}{2} = 154 {cm}^{2}∴Areaofonecircle→
2
308
=154cm
2
\sf\longrightarrow \pi {r}^{2} = 154 {cm}^{2}⟶πr
2
=154cm
2
\sf\longrightarrow \dfrac{22}{7} {r}^{2} = 154⟶
7
22
r
2
=154
\sf\longrightarrow {r}^{2} = 154 \times \dfrac{7}{22}⟶r
2
=154×
22
7
\sf\longrightarrow {r}^{2} = {\cancel {154}} \times \dfrac{7}{{\cancel {22}}}⟶r
2
=
154
×
22
7
\sf\longrightarrow {r}^{2} = 7 \times 7⟶r
2
=7×7
\sf\longrightarrow {r}^{2} = 49⟶r
2
=49
\sf\longrightarrow r = \sqrt{49}⟶r=
49
\sf\longrightarrow r = 7⟶r=7
.°. Radius of one circle is = 7 cm
Diameter of one circle => Breadth of the rectangle = (2 × 7) cm = 14 cm
Diameter of two circles => Length of the rectangle = (14 × 2) cm = 28 cm
Now,
\sf\underline {Area \: of \: rectangle \: = \: (length \times breadth) \: {unit}^{2}}
Areaofrectangle=(length×breadth)unit
2
\sf\longrightarrow (14 \times 28) {cm}^{2}⟶(14×28)cm
2
\sf\therefore 392 {cm}^{2}∴392cm
2
Hence, the area of the rectangle is 392 cm².