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Home Question Bank Math Geometry Archive 2024 December 26

Geometry Questions from Dec 26,2024

Browse the Geometry Q&A Archive for Dec 26,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Bookwork code: 4D Work out the volume of the wate in the cuboid-shaped container below. Give your answer in millilitres \( (\mathrm{ml}) \) and give any decimal answers to 1 d.p. (Hint: \( 1 \mathrm{ml}=1 \mathrm{~cm}^{3} \) ) What is the formula for calculating the surface area of a sphere? If the dimensions of a rectangular prism are doubled, how does that affect the surface area and volume? Example 7 What is the smallest number of terms of the geometrical progression, \( 8+24+72+\ldots \), that will give a total greater than 6000000 ? A sphere's diameter measures 12 inches. Calculate the surface area of the sphere. 3. The point, \( (O, O) \), also called the \( x \)-axis and the \( y \)-axis intersect. Esercizio 12.5 Determinare le equazioni parametriche e cartesiane della retta passante per i punti \( A \) e \( B \), dove; \( \begin{array}{l}\text { (i) } A=(-1,-1,0) \quad B=(-3,1,0) \\ \text { (ii) } A=(2,1,2) \quad B=(1,1,-1) \\ \text { (iii) } A=\left(\frac{3}{2}, \frac{8}{5}, 1\right) \quad B=\left(-\frac{1}{2}, \frac{1}{5}, 3\right)\end{array} \) Esencrio 12.2 Stabilire se i punti \( A, B, C \in A^{3}(\mathbb{R}) \) sono allineati. In caso altermativo, determinare la retta che passa per ensi, in caso negativo il piano che li oontiene: (h) \( A=(3,0,-2) \quad B=(4,-1,-4) \quad C=(2,1,0) \); (ii) \( A=(2,2,2) \quad B=(1,1,-1) \quad C=(-1,2,3) \); EsERCIzIo 12.2 Stabilire se i punti \( A, B, C \in \mathbb{A}^{3}(\mathbb{R}) \) sono allineati. In caso affermativo, leterminare la retta che passa per essi, in caso negativo il piano che li contiene: ( \( A=(3,0,-2) \quad B=(4,-1,-4) \quad C=(2,1,0) \) На окружности с центром \( O \) выбрана точка \( A \). Случайным образом бросают точку \( X \) на эту окружность. Найдите вероятность того, что угол \( A O X \) больше \( 120^{\circ} \). 1. 0,25 2. \( \frac{1}{3} \) 3. 0,5 4. \( \frac{2}{3} \) 5. 0,75 6. \( \frac{1}{6} \) 7. \( \frac{5}{6} \)
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