Volume and Surface Areas Quiz Set 005

By Pythagorean theorem, the radius of base = $√{41^2 - 9^2}$ = $√{1681 - 81}$ = 40. The volume is π × r × l = π × 40 × 41 = 1640π sq. m.

The volume of the pipe is π × (15² - 13²) × 42, which is $22/7$ × 56 × 42. Weight = vol × density = $22/7$ × 56 × 42 × 3 = 22176 gm.

One of the right triangles of the isosceles triangle has its base = 32/2 = 16. By Pythagorean theorem, the height = $√{34^2 - 16^2}$ = $√{1156 - 256}$ = 30. The radius of the base of the cone r = 16 cm, and height h = 30 cm. The volume is $1/3$π$(r^2 × h)$ = $1/3$π$(16^2 × 30)$ = 2560π.

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 = ${93/41}$, which is same as: $2{11/41}$.

The height of the can will be filled to 4 cm. The volume of collected water is same as the volume of cylinder with radius 8 cm and height 4 cm., which equals π8² × 4 = 256π cu. cm.