Geometry Q&A Archives - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day

Determine whether the planes are parallel, perpendicular, or neither. If the planes are neither parallel nor perpendicular, find the angle between them.

2x + 3y + z = […]

Find the length and width of a rectangle that has the given area and a minimum perimeter.

Area of Rectangle A = 49 ft^(2) The aim of this article is to find the dimensions of a rectangle whose area A is known and it is assumed that it has the minimum perimeter P. The basic […]

The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the Solid.

This question aims to find the volume of the solid whose base forms an elliptical region. The cross-section perpendicular to the x-axis forms isosceles right triangles with hypotenuse as seen in the line shown in Figure 1. The concept of this question is based on the basic geometry of shapes like the area and volume […]

Show that the equation represents a sphere and find its center and radius.

$x^2+y^2+z^2+8x-6y+2z+17=0$ The main objective of this question is to prove that the given equation is for a sphere and also to find the center and radius for a given sphere equation. This question uses the concept of the sphere. A sphere is a round, three-dimensional object like a ball or moon where each point on its […]

Estimate the angle to the nearest one-half radian.

Figure (1): Angle given in the question statement Read moreIdentify the surface whose equation is given. ρ=sinθsinØThe aim of this question is to develop the ability to estimate angles to the nearest half radian just by visualizing them. To estimate such angles, we need to imagine a circular scale of our choice in accordance with […]