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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 The 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 our required precision. If we choose a circular […]

Which pair of angles has congruent values for the sinx° and the cosy°?

Part(a) $35^{circ};55^{circ}$ Part(b) $35^{circ};145^{circ}$ Part(c) $35^{circ};70^{circ}$ Part(d) $35^{circ};35^{circ}$ This question aims to find the pair of angles concurrent to the sin x and cos y. Congruent angles are the angles that have the same measure. So all angles that have the same size will be called congruent angles. They are seen everywhere, such as in equilateral triangles, isosceles triangles, […]

Co-planar circles that have a common center are called:

What type of circles are present in the figure? – Common Circles – Tangent Circles – Congruent Circles – Concentric Circles The question aims to find what to call two circles that are in the same plane and have the same center point. The question depends on the circle geometry concerning the similarity between circles. […]