Question : The difference between the areas of two concentric circles is 264 cm2. What is the difference between the square of their radius? (use $\pi=\frac{22}{7}$)
Option 1: 70
Option 2: 140
Option 3: 84
Option 4: 64
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Correct Answer: 84
Solution : Given: The difference between the areas of two concentric circles is 264 cm2. The area of the circle $=\pi R^2$ where $R$ is the radius. According to the question, $\pi R^2–\pi r^2=264$ ⇒ $\frac{22}{7}\times(R^2–r^2)=264$ ⇒ $(R^2–r^2)=\frac{264\times 7}{22}$ ⇒ $R^2–r^2=\frac{1848}{22}=84$ Hence, the correct answer is 84.
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Question : Four circles of equal radii are described around the four corners of a square so that each touches two of the other circles. If each side of the squares is 140 cm, then the area of the space enclosed between the circumference of the circle is: (Take $\pi=\frac{22}{7}$)
Option 1: 4200 cm2
Option 2: 2100 cm2
Option 3: 7000 cm2
Option 4: 2800 cm2
Question : The volume of a sphere of radius 4.2 cm is: (Use $\pi=\frac{22}{7}$)
Option 1: 278.234 cm3
Option 2: 312.725 cm3
Option 3: 297.824 cm3
Option 4: 310.464 cm3
Question : The radius of a large solid sphere is 14 cm. It is melted to form 8 equal small solid spheres. What is the sum of the total surface areas of all 8 small solid spheres? (use $\pi=\frac{22}{7}$)
Option 1: 3648 cm2
Option 2: 4928 cm2
Option 3: 4244 cm2
Option 4: 4158 cm2
Question : The curved surface area of a solid hemisphere is 22 cm2. What is the total surface area of the hemisphere? (use $\pi=\frac{22}{7}$)
Option 1: 66 cm2
Option 2: 44 cm2
Option 3: 33 cm2
Option 4: 30 cm2
Question : If the slant height of a cone is 60 cm and the radius of its base is 21 cm, then find its curved surface area is? (use $\pi=\frac{22}{7}$)
Option 1: 3880 cm2
Option 2: 3820 cm2
Option 3: 3960 cm2
Option 4: 4020 cm2
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