A solid cylinder of radius 5 cm is drilled by four cylindrical holes, each of radius 1 cm and length equal to the full height. The volume removed is approximately what percent?
16%
Let the height of the cylinder be \(h\).
Step 1 – volume of the original cylinder:
\(V = \pi (5)^{2} h = 25\pi h\)
Step 2 – total volume removed by 4 holes (each is itself a small cylinder of radius 1 cm and height \(h\)):
\(V_{\text{removed}} = 4 \times \pi (1)^{2} h = 4\pi h\)
Step 3 – percent removed:
\(\dfrac{V_{\text{removed}}}{V} \times 100 = \dfrac{4\pi h}{25\pi h} \times 100 = \dfrac{4}{25} \times 100 = 16\%\)
Hence the volume removed is approximately 16%.
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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 = \(22\over7\)]
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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:
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