A decorative column is made in the shape of a regular hexagonal prism. The side length of its base is 10 cm. The column is built from multiple sections, and their heights form an arithmetic progression: the first section is 5 cm tall, and each subsequent section is 2 cm taller than the previous one. If the column has 4 sections in total, what is the total volume of the column?
4800√3 cm³
Section heights (AP: a=5, d=2, n=4): 5, 7, 9, 11 cm
Total height: \(5+7+9+11 = 32\) cm
Base area of regular hexagon (side = 10 cm):
\(A = \dfrac{{3\sqrt{{3}}}}{{2}} \times 10^2 = 150\sqrt{{3}}\) cm²
Total Volume:
\(V = A \times h_{{\text{{total}}}} = 150\sqrt{{3}} \times 32 = \mathbf{{4800\sqrt{{3}}}}\) cm³
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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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(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:
