9. Volume NOTES.notebook January 19, 2017
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1 Starter - NO Calculators ) Find 20% of 248 2) Find Today's Learning: ) Find the highest common factor of 4 and 49. To revise volume of cubes, cuboids and prisms. 4) Find 5% of 80. 5) Calculate ) Find the volume of this cube in cm : 2) Find the volume of this carton in ml: ) If the volume of this cuboid is 42 ml, find its height. Calculate the total volume of the object: 5 mm 2cm cm 6cm 4 cm
2 Volume of Prisms A prism has the same cross-section all the way through its height. Volume = cross section area x height E.g. ) 0cm Find the volume of these objects: ) 4 cm 0 cm 2) 0 cm 2 cm 7 cm 8 cm 6cm Area = 8cm 2 Starter 2g ) Solve for g: + = 2g + 6 Volume of a Cylinder 2) Without a calculator, find 0.4 x. V = πr 2 h r ) Calculate 2 + ( + 2 ) - x 6 Example : *not given in exams Find the volume in litres, to sig. fig. h 50cm 70cm 4) If all the numbers from to 20 are written on cards, and I pick a card at random, what is the probability that the number I pick is prime? 5) Multiply out and simplify: 2T - 2(T + - T)
3 2) Find the volume of the trough in litres, correct to 2 d.p. 24 cm. 5 m This is a section of a water pipe. The inside of the pipe has a diameter of 7 cm. How much water can this pipe hold? 2 cm. 2 m Starter: Find someone who can tell you the answer... ) Without a calculator, find 0.2 x.2 2) Factorise m 2-4m ) Multiply out the brackets: 4T( - 2T) 4) List all the primes between 0 and 20 write down the answer and the person's name 5 cm Find the radius of the can. 5) Find the product of a half and a quarter V = 500 cm 6) Round.0472 to significant figures 7) Take 0% off ) Divide 500 by 0.5
4 Challenge: This wrapper is curved around a can so its edges just meet. What is the volume of the can? Today's Learning: Yummy Dog Food 0 cm To calculate the volume of any cone. 8 cm Volume of a Cone 2) Calculate the volume of this shape. h r V = e.g. ) Calculate the volume of this cone. πr 2 h *given in exams 28 cm 5 cm 42 cm 0 cm 20 cm
5 h 8 cm This cone can hold 2 litres. Calculate the height of the cone. Volume of a Sphere 4 V = πr e.g. ) Find the volume of this sphere. e.g. 2) Find the volume of this hemisphere. Find the volume of this object, made up of a hemisphere, a cylinder and a cone: 4 cm 28 cm 8 cm 20 cm
6 Starter ) Multiply out the brackets: T(2 - T) The volume of this sphere is 489 cm. Calculate the radius of this sphere. 2) Factorise by taking out a common factor: 4mn + 2m 2 ) Calculate ) Calculate x 5 5) Calculate 2. x 4 Volume of a Pyramid V = x base area x perpendicular height A cylindrical beaker shown on the left is full of water. If the water is poured into the beaker on the right, will it overflow? e.g. ) Find the volume of this square based pyramid. 2 cm 8 cm 2 cm 8 cm cm
7 The rectangular block of metal shown is melted down to make metal balls with radius cm. How many balls can be made? A paperweight is made of solid plastic. It's height must be 6 cm. The manufacturer must decide between the cone and pyramid shown. Which one requires less plastic to make? 45 cm cm 60 cm 0 cm 5 cm Starter ) Multiply out the brackets: b(e + 2) 2 2) Without a calculator, calculate - 8 ) Find the lowest common multiple of 2 and 0. 4) Decrease 200 by 45% 5) If the numbers to 00 are written on cards, and I pick one out at random, what is the probability the card has a 9 on it?
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11.8 Start Thinking You buy a friend a basketball as a gift. You want to construct a container to put the ball in to disguise it when it is wrapped. You construct the two containers shown in the diagram.