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Home Question Bank Math Geometry Archive 2025 January 03

Geometry Questions from Jan 03,2025

Browse the Geometry Q&A Archive for Jan 03,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Question 2: \( \triangle A B C \cong \triangle D E F, B C=3 p+18 \), and \( E F=5 p-4 \). Find \( p \) and \( E F \). - Since the triangles are congruent: \( B C=E F \). - Set up the equation: \( 3 p+18=5 p-4 \). - Solve for \( p \) : \( 18+4=5 p-3 p \), \( 22=2 p \), \( p=11 \). - Substitute \( p=11 \) into \( E F=5 p-4 \) : \( E F=5(11)-4=55-4=51 \). Answer: \( p=11, E F=51 \). The measures of the angles of a triangle are in the ratio of \( 7: 8: 9 \). What are the measures of the angles? - The sum of angles in a triangle \( =180^{\circ} \). - Add the ratio parts: \( 7+8+9=24 \). - Find the value of one part: \( 180 \div 24=7.5 \). - Multiply each part of the ratio by 7.5 : - \( 7 \times 7.5=52.5^{\circ} \), - \( 8 \times 7.5=60^{\circ} \), - \( 9 \times 7.5=67.5^{\circ} \). Answer: \( 52.5^{\circ}, 60^{\circ}, 67.5^{\circ} \). El valor positivo que debe tomar \( x \) para que la distancia entre los puntos \( A(-1,2) \) y \( B(x, 10) \) sea igual a 10 es: \( \begin{array}{llll}\text { a) } 2 & \text { b) } 10 & \text { c) } 5 & \text { d) } 2\end{array} \) A water reservoir in the form of a cone mounted on a hemisphere is built such that the plane face of the hemisphere fit exactly to the base of the cone and the height of the cone is 6 times thr radius o its base. (a) Illustrate this information in a diagram. (b) If the volume of the reservoir is \( 333 \frac{1}{3} \pi m^{3} \), calculate, correct to the nearest whole number, the : (I) volume of the hemisphere ; (II) Total A sphere has a radius of 5 cm. What is its volume? A right triangle has one leg that measures 8 units and the other leg measures 6 units. Calculate the length of the hypotenuse. 1. COORDINATE GEOMETRY Classify \( \triangle A B C \) with vertices \( A(-2,-1), B(-1,3) \) and \( C(2,0) \) as scalene, equilateral, or isosceles. Un solide a une section transversale constante qui est un demi-cercle avec un rayon de 3. Quelle est la formule pour trouver le volume de ce solide si sa longueur est de 5? Esercizio 3. Nello spazio euclideo tridimensionale sono dati il piano e la retta seguenti: \[ \pi: z=3 \quad \text { e } \quad r:\left\{\begin{array}{l}x=0 \\ y=t \\ z=1\end{array}\right. \] Trovare, se esiste, una sfera col centro su \( r \), tangente a \( \pi \) e passante per l'origine. A composite solid consists of a cylinder and a hemisphere on top. The cylinder has a height of 8 inches and a radius of 3 inches. What is the total surface area of the composite solid if the hemisphere is attached to the top?
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