A composite solid is formed by placing a cone, which has a radius of 2 cm and a height of 6 cm, on top of a right circular cylinder. The cylinder's radius is twice that of the cone, and its height is also double that of the cone. What is the ratio of the volume of the cone to that of the cylinder?
1:24
Volume of the cone = \(\frac{1}{3}\pi r^2 h = \frac{1}{3}\pi \times 2^2 \times 6 = 8\pi\) cm3.
Cylinder radius = 4 cm and height = 12 cm, so its volume = \(\pi \times 4^2 \times 12 = 192\pi\) cm3.
Ratio = \(8\pi : 192\pi = 1 : 24\).
Hence, the ratio of the volume of the cone to that of the cylinder is 1:24.
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Important Questions from 3-D Mensuration
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(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
The length and breadth of a cuboid are 50 cm and 75 cm, respectively. If the length of the diagonal is $17\sqrt{29}$ cm, then what is the volume (in $cm^{3}$) of the cuboid?
