A display stand is shaped like a right triangular prism. The triangular base is a right-angled triangle with perpendicular sides measuring 3 cm and 4 cm. The height of the prism is 10 cm. What is the ratio of the area of the largest rectangular face to the area of the smallest rectangular face of the prism?
5:3
The triangular base is right-angled with legs 3 cm and 4 cm, so its hypotenuse is \(\sqrt{3^2+4^2} = \sqrt{9+16} = \sqrt{25} = 5\) cm.
The three rectangular faces of the prism have areas equal to each side of the triangle multiplied by the prism's height of 10 cm.
These areas are \(3 \times 10 = 30\) cm², \(4 \times 10 = 40\) cm², and \(5 \times 10 = 50\) cm².
The largest face is 50 cm² and the smallest is 30 cm², so the ratio is \(\frac{50}{30} = \frac{5}{3}\).
Hence, the answer is 5:3.
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Important Questions from 3-D Mensuration
- Find the surface area of a sphere whose diameter is equal to 98 cm.
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- A solid metallic sphere of radius 10 cm is melted and recast into 125 identical spheres. What is the ratio of the surface area of the original sphere to the total surface area of 6 smaller spheres so formed?
- Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm. Use $\pi = \frac{22}{7}$
- The volume of a solid cylinder is 5852 cm³ and its height is 38 cm. What is the total surface area of the solid cylinder? (Round your answer to the nearest integer) (Use $\pi = \frac{22}{7}$)
