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Home Question Bank Math Geometry Archive 2024 December 29

Geometry Questions from Dec 29,2024

Browse the Geometry Q&A Archive for Dec 29,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A Cone has a Eircular bases a perpen- dicular height of 42 cm , and a serni-vertical angle of \( 30^{\circ} \). calculate the slant height of the cone C) Simplifiez les expressions suivantes au maximum (les lettres représentent des points du plan ou de l'espace): \( \begin{array}{lll}\text { 1) } \overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D} & \text { 2) } \overrightarrow{A B}-\overrightarrow{B C}+2 \overrightarrow{E D}-\overrightarrow{D E} & \text { 3) } \overrightarrow{O M}+\overrightarrow{O N}+\overrightarrow{O P}\end{array} \) straight lines. Are \( W X \) and \( Y Z \) parallel? Give reason. The volume of a composite shape made up of a cube with a side length of 4 cm and a cylindrical hole of radius 1 cm running through it vertically is needed. Calculate the resulting volume. 3.3. A l'aide de l'égalité choisie à la question précédente, calculer la longueur [OP]. 3.4. L'artisan engagé sur le pare considère qu'il faut un pilier de 5 mètres. A-t-il raison ? Rédiger la réponse. Les côtés \( [\mathrm{OP}] \) et \( [\mathrm{CB}] \) sont parallèles. Laquelle de ces trois égalités est vérifiće ? Cocher la case correspondant à la bonne réponse. \( \frac{\mathrm{AP}}{\mathrm{PB}}=\frac{\mathrm{OP}}{\mathrm{CB}} \) \( \square \frac{\mathrm{AP}}{\mathrm{AB}}=\frac{\mathrm{OP}}{\mathrm{CB}} \) Determina per quali valori di \( k \) le rette del fascio di equazione \( k x+(k+1) y-1=0 \), intersecano: il segmento \( A B \) di estremi \( A(1,1), B(0,2) \); il segmento \( A P \) di estremi \( A(1,1), P(-1,-1) \); la poligonale \( O A B \), essendo \( O(0,0), A(1,1), B(0,2) \). \( \left[\right. \) a. \( -\frac{1}{2} \leq k \leq 0 ; \) b. \( k \leq-1 \cup k \geqslant \) 3. (a) Mutassunk példát olyan sokszögre, amelynek minden oldala egyenlő hosszú és minden oldala pontosan 2 másik oldalával párhuzamos. Adjuk meg a sokszög összes szögét. (b) Mutassunk példát olyan sokszögre, amelynek minden oldala egyenlö hosszú és minden oldala pontosan 3 másik oldalával párhuzamos. Adjuk meg a sokszög összes szögét. A sokszögnek nem lehet sem \( 0^{\circ} \)-os, sem \( 180^{\circ}-o s \) szöge. A sokszög nem metszhetı önmagát, azaz a nem szomszédos oldalainak nem lehet közös pontja. 2. A company has been asked to design a building for an athletic event. The building is in the shape of a square pyramid. The pyramid has a height of 481 feet, and the length of each side of the base is 756 feet. What is the approximate volume of the pyramid? \( 1.21 \times 10^{5} \mathrm{ft}^{3} \) \( 4.85 \times 10^{5} \mathrm{ft}^{3} \) \( 9.16 \times 10^{7} \mathrm{ft}^{3} \) \( 2.75 \times 10^{8} \mathrm{ft}^{3} \) Câu 8. Dình Yên Thái (phường Hàng Gai, quận Hoàn Kiếm, Hà Nội) là nơi thờ Nguyên phi Y̌ Lan. Trong đình hiện còn giếng cỗ khơ mạch từ năm 1063, đến nay nước vẫn còn trong mát. Miệng giếng là một hình tròn có đường kính 66 cm . Người ta xây thành giếng rộng 22 cm bao quanh miệng giếng. Tính diện tích của thành giếng. (1 điểm)
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