The curved surface area of a solid cylinder is numerically equal to the total surface area of another cylinder whose radius is half of the first cylinder. If the height and radius of the first cylinder are 7 cm and 4 cm, respectively, find the curved surface area of the second cylinder.
\(48\pi\) cm2
Curved surface area of a cylinder is \(2\pi r h\), and total surface area is \(2\pi r (h + r)\).
First cylinder has \(r_1 = 4\) cm and \(h_1 = 7\) cm, so its CSA \(= 2\pi (4)(7) = 56\pi\).
The second cylinder's radius is half of the first: \(r_2 = \frac{4}{2} = 2\) cm. Let its height be \(h_2\).
Its TSA \(= 2\pi r_2 (h_2 + r_2) = 2\pi (2)(h_2 + 2)\).
Set the first cylinder's CSA equal to the second cylinder's TSA: \(2\pi(2)(h_2 + 2) = 56\pi \Rightarrow 4(h_2 + 2) = 56 \Rightarrow h_2 + 2 = 14 \Rightarrow h_2 = 12\) cm.
Curved surface area of the second cylinder \(= 2\pi r_2 h_2 = 2\pi (2)(12) = 48\pi\) cm2.
Hence, the curved surface area of the second cylinder is \(48\pi\) cm2.
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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:
