Q.If the height and diameter of a right circular cylinder are equal, and its volume is 2156 cubic cm, then find the radius. (a) 5 cm (b) 6 cm (c) 7 cm (d) 9 cm
Answer: C
Let the diameter of the right circular cylinder be equal to its height, \( h \) cm. \(\therefore\) Radius \( = \cfrac{h}{2} \) cm. By the given condition: \[ \pi \times \left(\cfrac{h}{2}\right)^2 \times h = 2156 \] \[ \cfrac{22 \times h^2 \times h}{7 \times 4} = 2156 \] \[ h^3 = \cfrac{2156 \times 28}{22} \] \[ h^3 = 98 \times 28 = 2 \times 7 \times 7 \times 7 \times 2 \times 2 \] \[ h = 2 \times 7 = 14 \] \(\therefore\) Radius \( = \cfrac{14}{2} \) cm \( = 7 \) cm.
Similar Questions