Q.1.A) Solve any four sub-questions from following: 1) \( \frac{1 \text { litre }}{}=-\mathrm{cm}^{3} \) 2) In \( \triangle X Y Z \) which is the angle opposite to side \( X Y \). 3) What is the measure of semicircle? 4) If Amount \( =? 7990 \), Principal \( =? 5000 \), then find compound interest. 5) In a circle with centre ' \( C \) '. Seg \( A B \) is a chord of length \( 7 \mathrm{~cm} \). seg \( \mathrm{CD} \perp \) chord \( \mathrm{AB} \). then find \( \ell(\mathrm{DB}) \). 6) Write the formula of volume of cylinder. B) Solve any two sub-questions from following: 1) Divide, Write quotient and remainder: \( \left(y^{2}+8 y+15\right) \div(y+3) \) (4) B Marks : 50 B Marks : 50 (4) ? ? ? \( \qquad \) \( \qquad \) \( \qquad \) - ? (
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Solve each problem. See Examples 1-4 Volume of a Cylinder The volume of a right circular cylinder is jointly proportional to the square of the radius of the circular base and to the height. If the volume is $300 \mathrm{~cm}^{3}$ when the height is $10.62 \mathrm{~cm}$ and the radius is $3 \mathrm{~cm},$ find the volume, to the nearest tenth, of a cylinder with radius $4 \mathrm{~cm}$ and height $15.92 \mathrm{~cm} .$
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Give clear and complete answers to the following problems and questions. Write your explanations clearly using complete sentences. Include diagrams whenever appropriate. Use the given information to find (if possible) the remaining sides and angles of $\triangle A B C .$ If two solutions exist, find both. If no solution exists, explain how you know this. a. $A=\frac{\pi}{6}, B=\frac{\pi}{4}, a=10$ units b. $A=\frac{\pi}{3}, B=\frac{\pi}{18}, b=4.5 \mathrm{cm}$ c. $A=\frac{5 \pi}{6}, C=\frac{\pi}{9}, a=200$ units d. $A=100^{\circ}, a=125 \mathrm{cm}, b=10 \mathrm{cm}$ e. $C=\frac{2 \pi}{3}, a=4$ inches, $b=6$ inches f. $A=58^{\circ}, a=4.5 \mathrm{cm}, b=12.8 \mathrm{cm}$ g. $A=58^{\circ}, a=4.5 \mathrm{ft}, b=5 \mathrm{ft}$ h. $A=110^{\circ}, a=125 \mathrm{cm}, b=200 \mathrm{cm}$
Calculate answers to the following problems, and check your solutions by making ballpark estimates. (a) The melting point of gold is $1064^{\circ} \mathrm{C}$ . What is this temperature in degrees Fahrenheit? (b) How large, in cubic centimeters, is the volume of a red blood cell if the cell has a cylindrical shape with a diameter of $6 \times 10^{-6} \mathrm{m}$ and a height of $2 \times 10^{-6} \mathrm{m} ?$
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