Volume and Surface Areas Quiz Set 011

In one hour, a water column of length 10 km is delivered through the cylindrical pipe. The equivalent volume is ${22 × 49 × 49 × 10 × 1000}/{7 × 100 × 100}$, which can easily be cancelled to get 7546 cu. m.

The wire is a cylinder with r = 1/10 cm, and length L. The volume of tin is equal to the volume of the wire. So π ${1/10} × {1/10} × L$ = 88, which gives L = ${10 × 10 × 88 × 7}/22$ = 2800 cm.

The well-known relation for a cube is $S/V = 6/a$, which can be re-arranged to get $a = 6 × V/S$ = ${138/41}$, which is same as: $3{15/41}$.

Let h be the height, and l and b be the length and breadth. We are given lb + lb = lh + hb + lh + hb. Combining the terms and cancelling 2, we get lb = h(l + b), which gives h = ${lb}/{l + b}$ = ${47 × 29}/{47 + 29}$ = ${1363/76}$, which is same as: $17{71/76}$ m.

The height of the can will be filled to 7 cm. The volume of collected water is same as the volume of cylinder with radius 1 cm and height 7 cm., which equals π1² × 7 = 7π cu. cm.