Mensuration

The correct option is (C) :400 m².

Let the diagonals of the rhombus be and . Given, one diagonal cm and the area of the rhombus cm . The area of a rhombus is given by the formula: $ . Half the lengths of the diagonals are cm and cm. By the Pythagorean theorem, the side of the rhombus can be found using the right-angled triangle formed by half of each diagonal: \) . \) $ Therefore, the perimeter of the rhombus is 68 cm.

The volume of the original large sphere: Let the radius of each smaller sphere be . Since the large sphere is divided into 8 equal smaller spheres, total volume is conserved: Divide both sides by : Thus, each smaller sphere has radius 10 cm.

The volume of a cube is given by , where is the side length. Given that cm³, The diagonal of a cube is the space diagonal, which can be found using the Pythagorean theorem in three dimensions: This diagonal represents the longest distance between two opposite vertices of the cube.

- (A) Volume of cone = (Formula for cone's volume)
- (B) Curved surface area of cylinder = (Lateral surface area without bases)
- (C) Total surface area of cone = (Sum of base area and curved surface)
- (D) Volume of sphere = (Complete volume formula)