A solid cylinder has a radius of 5 cm and a height of 10 cm. A smaller cylindrical hole of radius 3 cm is drilled coaxially through its entire length. What is the approximate volume of the remaining solid?
502 cm³
The remaining solid is a hollow cylinder. Its volume equals the outer cylinder's volume minus the drilled (inner) cylinder's volume.
Step 1 — volumes:
\(V_{\text{outer}} = \pi R^2 h = \pi (5)^2 (10) = 250\pi\)
\(V_{\text{hole}} = \pi r^2 h = \pi (3)^2 (10) = 90\pi\)
Step 2 — remaining volume:
\(V = (250 - 90)\pi = 160\pi\)
Step 3 — numerical value:
\(V \approx 160 \times 3.1416 \approx 502.65 \text{ cm}^3\)
The closest option is 502 cm³ — option (3).
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Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(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:
