Volume and Surface Areas Quiz Set 016

Let the dimensions of the cuboid be L, 2L and L. Its total surface area is 2(L × 2L + 2L × L + L × L) = 10L². When it is placed on the table, the bottom face is hidden, so net visible area is 10L² - 2L² = 8L². When the cubical block of side L is placed on this block its(i.e., cube's) own L² and L² of the cuboidal block is hidden. So it hides 2L². Thus, the net visible is 8L² + 6L² - 2L² = 12L² = 12 × 8² = 768 sq. units.

Let R be the radius. Then $V/S = {4/3 × \text"π" × R^3}/{4 × \text"π" × R^2}$ = $R/3$, so R = 3 × ratio = ${69/17}$, which is same as: $4{1/17}$.

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is π × ${7 × 7 × 10 × 1000}/{100 × 100}$, which can easily be cancelled to get 49π cu. m.

By Pythagorean theorem, the radius of base = $√{17^2 - 15^2}$ = $√{289 - 225}$ = 8. The volume is π × r × l = π × 8 × 17 = 136π sq. m.

Let the radius of the sphere be R. The volumes are equal. So $4/3$ π R³ = $1/3$ π 12² × 6. Cancelling π/3 from both sides, R³ = ${12 × 12 × 6}/4$ = 216 = 6³. So R = 6 cm.