The surface area of a cube of length x is equal to the surface area of a sphere of radius y. Consider the following statements :<br>1. 2x \gt 3y<br>2. The volume of the cube is greater than the volume of the sphere.<br>Which of the above statements is/are correct?

Explanation

Given 6x^2 = 4\pi y^2, so x^2 = \frac{2\pi}{3} y^2 \approx 2.09 y^2, giving x \approx 1.44 y. Comparing 2x and 3y, 2(1.44y) = 2.88y, which is not greater than 3y (Statement 1 false). For a given surface area, a sphere encloses the maximum volume. Therefore, the volume of the cube is less than the sphere (Statement 2 false).

Related questions on Mensuration

• A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
• A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
• A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
• A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
• Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...