Date | November 2016 | Marks available | 4 | Reference code | 16N.1.sl.TZ0.7 |
Level | SL only | Paper | 1 | Time zone | TZ0 |
Command term | Calculate | Question number | 7 | Adapted from | N/A |
Question
A balloon in the shape of a sphere is filled with helium until the radius is 6 cm.
The volume of the balloon is increased by 40%.
Calculate the volume of the balloon.
Calculate the radius of the balloon following this increase.
Markscheme
Units are required in parts (a) and (b).
43π×63 (M1)
Note: Award (M1) for correct substitution into volume of sphere formula.
=905 cm3 (288π cm3, 904.778… cm3) (A1) (C2)
Note: Answers derived from the use of approximations of π (3.14; 22/7) are awarded (A0).
[2 marks]
Units are required in parts (a) and (b).
140100×904.778…=43πr3 OR 140100×288π=43πr3 OR 1266.69…=43πr3 (M1)(M1)
Note: Award (M1) for multiplying their part (a) by 1.4 or equivalent, (M1) for equating to the volume of a sphere formula.
r3=3×1266.69…4π OR r=3√3×1266.69…4π OR r=3√(1.4)×63 OR r3=302.4 (M1)
Note: Award (M1) for isolating r.
(r=) 6.71 cm (6.71213…) (A1)(ft) (C4)
Note: Follow through from part (a).
[4 marks]
Examiners report
Syllabus sections
- 16N.2.sl.TZ0.6d: Show that A=πr2+1000000r.
- 18M.1.sl.TZ2.15b: The total external surface area of the pencil case rounded to 3 significant figures is 570...
- 18M.1.sl.TZ2.15a: Find an expression for the slant height of the cone in terms of r.
- 18M.2.sl.TZ1.1f: Calculate the total length of metal required for one support.
- 18M.2.sl.TZ1.1e: Show that Farmer Brown is incorrect.
- 18M.2.sl.TZ1.1d: Calculate the length of AE.
- 18M.2.sl.TZ1.1c: Calculate the length of MN.
- 18M.2.sl.TZ1.1b: Calculate the total volume of the barn.
- 18M.2.sl.TZ1.1a: Calculate the area of triangle EAD.
- 18M.2.sl.TZ1.6f: The designer claims that the new trash can has a capacity that is at least 40% greater than...
- 18M.2.sl.TZ1.6e: Using your graphic display calculator, find the value of r which maximizes the value of V.
- 18M.2.sl.TZ1.6c: Find the height of the cylinder, h , of the new trash can, in terms of r.
- 18M.2.sl.TZ1.6b: Find the total volume of the trash can.
- 18M.2.sl.TZ1.6a: Write down the height of the cylinder.
- 18M.1.sl.TZ1.14c: Calculate the curved surface area of the remaining solid.
- 18M.1.sl.TZ1.14b: Calculate the curved surface area of the cone which has been removed.
- 18M.1.sl.TZ1.14a: Calculate the radius of the base of the cone which has been removed.
- 17M.1.sl.TZ2.12b: Find the value of h.
- 17M.1.sl.TZ2.12a: Find the volume of water in the container.
- 17M.2.sl.TZ1.4f: In the context of this model, state what the value of 19 represents.
- 17M.2.sl.TZ1.4e: Calculate, to the nearest second, the time since the pizza was taken out of the oven until it...
- 17M.2.sl.TZ1.4d: Find the temperature that the pizza will be 5 minutes after it is taken out of the oven.
- 17M.2.sl.TZ1.4c: Find the value of a.
- 17M.2.sl.TZ1.4b: Find the radius of the sphere in cm, correct to one decimal place.
- 17M.2.sl.TZ1.4a: Calculate the volume of this pan.
- 17M.1.sl.TZ1.9c: Find the curved surface area of the cone.
- 17M.1.sl.TZ1.9b: Find the slant height, l, of the cone.
- 17M.1.sl.TZ1.9a: Find the radius, r, of the circular base of the cone.
- 16M.2.sl.TZ2.4f: Calculate the maximum number of cups that can be completely filled with the...
- 16M.2.sl.TZ2.4e: Chavi is celebrating her birthday with her friends on the playground. Her mother brings a...
- 16M.2.sl.TZ2.4d: Chavi estimates that the height of the tree is 6m. Calculate the percentage...
- 16M.2.sl.TZ2.4c: There is a tree at C, perpendicular to the ground. The angle of elevation to the...
- 16M.2.sl.TZ2.4b: Calculate angle ADC.
- 16M.2.sl.TZ2.4a: A playground, when viewed from above, is shaped like a quadrilateral, ABCD,...
- 16M.1.sl.TZ2.11c: Dan is going to paint the curved surface and the base of the snack container. Calculate the...
- 16M.1.sl.TZ2.11b: Calculate the area of the base of the container.
- 16M.1.sl.TZ2.11a: A snack container has a cylindrical shape. The diameter of the base is 7.84cm....
- 16M.1.sl.TZ2.1b: The surface area of the Earth that is covered by water is approximately...
- 16M.1.sl.TZ2.1a: Assume that the Earth is a sphere with a radius, r , of...
- 16M.2.sl.TZ1.4f: Ahmad and his friends like to sit in the pyramid’s shadow, ABW, to cool down.At...
- 16M.2.sl.TZ1.4e: Ahmad is a tour guide at the Great Pyramid of Giza. He claims that the amount of stone used...
- 16M.2.sl.TZ1.4d: Write down your answer to part (c) in the form a×10k where...
- 16M.2.sl.TZ1.4c: Find the volume of the pyramid.
- 16M.2.sl.TZ1.4b: Calculate the height of the pyramid, VO .
- 16M.2.sl.TZ1.4a: The Great Pyramid of Giza in Egypt is a right pyramid with a square base. The pyramid is made...
- 16M.1.sl.TZ1.4b: The price of tuna per cm3 is the same for each brand. A can of...
- 16M.1.sl.TZ1.4a: FreshWave brand tuna is sold in cans that are in the shape of a cuboid with length...
- 16N.2.sl.TZ0.6h: Find the least number of cans of water-resistant material that will coat the area in part (g).
- 16N.2.sl.TZ0.6g: Find the value of this minimum area.
- 16N.2.sl.TZ0.6f: Using your answer to part (e), find the value of r which minimizes A.
- 16N.2.sl.TZ0.6e: Find dAdr.
- 16N.2.sl.TZ0.6c: Write down, in terms of r and h, an equation for the volume of this water container.
- 16N.2.sl.TZ0.6b: Express this volume in cm3.
- 16N.2.sl.TZ0.6a: Write down a formula for A, the surface area to be coated.
- 16N.1.sl.TZ0.7a: Calculate the volume of the balloon.
- 10M.1.sl.TZ1.5a: Calculate the volume of the sphere. Give your answer correct to two decimal places.
- 10M.2.sl.TZ1.4e: Calculate the volume of the tower.
- 10N.1.sl.TZ0.3a: Find the volume of the box.
- 10N.1.sl.TZ0.12c: The height of the prism is 20 cm. Find the volume of the prism.
- 11N.1.sl.TZ0.9a: Calculate the volume of the observatory.
- 11N.1.sl.TZ0.9b: The hemispherical roof is to be painted. Calculate the area that is to be painted.
- 12N.1.sl.TZ0.4b: This circle is the base of a solid cylinder of height 25 cm. Write down the volume of the...
- 12N.1.sl.TZ0.4c: This circle is the base of a solid cylinder of height 25 cm. Find the total surface area of...
- 12N.2.sl.TZ0.3d: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle...
- 12N.2.sl.TZ0.3e: He next marks a fourth point, D, on the ground at a distance of 6 m from B , such that angle...
- 10M.2.sl.TZ2.4d: Find the volume of soil used.
- 12M.2.sl.TZ1.3c: Find the total surface area of the cylinder.
- 12M.2.sl.TZ1.3g: The cylinder was melted and recast into a solid cone, shown in the following diagram. The...
- 10M.2.sl.TZ2.5b.i: Find an expression for the curved surface area of the can, in terms of x. Simplify your answer.
- 12M.2.sl.TZ1.3b: Show that the volume of the metal used in the cylinder is 402 cm3, given correct to three...
- 12M.2.sl.TZ1.3d: The cylinder was melted and recast into a solid cone, shown in the following diagram. The...
- 12M.2.sl.TZ2.4c: Calculate the volume of the pyramid.
- 12M.2.sl.TZ2.5b: Show that the volume V m3 of the container is given by V = 24x2 − 6x3
- 12M.2.sl.TZ2.5g: The shipping container is to be painted. One litre of paint covers an area of 15 m2 . Paint...
- 09M.1.sl.TZ1.13b: Calculate the volume of the empty space in the tube when four tennis balls have been placed...
- 09M.1.sl.TZ1.13a: Find the volume of one tennis ball.
- 09M.2.sl.TZ1.4b: Find the total surface area of the chocolate bar.
- 09M.2.sl.TZ2.3f: A layer of earth 3 cm thick is removed from ABD. Find the volume removed in cubic metres.
- 11M.1.sl.TZ2.8a: Calculate the total volume of all 75 metal cannon balls excavated.
- 13M.1.sl.TZ2.1a: Calculate the exact value of the volume of the cuboid, in cm3.
- 13M.2.sl.TZ2.3d: Calculate the total surface area of the tent, including the base.
- 13M.2.sl.TZ2.3e: Calculate the volume of the tent.
- SPM.1.sl.TZ0.12b: Calculate the area that is painted red.
- SPM.2.sl.TZ0.2c: Calculate the volume of the office block.
- 07M.2.sl.TZ0.2i.a: Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal places.
- 07M.2.sl.TZ0.2i.c: (i) Jenny fills the cylinder with the number of balls found in part (b) and puts the lid on....
- SPM.2.sl.TZ0.6a: Calculate(i) the area of the base of the wastepaper bin;(ii) the height, h , of...
- SPM.2.sl.TZ0.6d: Show that the total external surface area, A , of the bin is...
- SPM.2.sl.TZ0.6b: State whether Nadia’s design is practical. Give a reason.
- SPM.2.sl.TZ0.6c: Write down an equation in h and r , using the given volume of the bin.
- SPM.2.sl.TZ0.6g: Determine whether Merryn’s design is an improvement upon Nadia’s. Give a reason.
- 07N.2.sl.TZ0.2a: Calculate the volume of the pyramid.
- 07N.2.sl.TZ0.2e: Calculate the total surface area of the pyramid.
- 08M.2.sl.TZ1.4ii.e: Find the volume of the pyramid.
- 08M.2.sl.TZ1.4ii.d: Find the total surface area of the pyramid.
- 08M.2.sl.TZ1.5ii.a: Show that 4x2+6xy=300.
- 08M.2.sl.TZ1.5ii.c: Hence show that the volume V of the box is given by V=100x−43x3.
- 08M.2.sl.TZ2.3ii.c: Calculate the volume of the pyramid.
- 08M.2.sl.TZ2.3ii.d: Daniel wants to make a rectangular prism with the same volume as that of Sylvia’s pyramid....
- 10M.2.sl.TZ2.5b.ii: Hence write down an expression for A, the total surface area of the can, in terms of x.
- 14M.1.sl.TZ2.4a: Find the volume of 1 chocolate.
- 14M.1.sl.TZ2.4c: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box...
- 14M.1.sl.TZ2.4d: The diagram shows the chocolate box from above. The 20 chocolates fit perfectly in the box...
- 14M.2.sl.TZ2.5a: Express the volume of the parcel in terms of l and w.
- 14M.2.sl.TZ2.6g: The water tank is shown below. It is partially filled with water. The water tank has a...
- 13N.2.sl.TZ0.2e: Show that the total surface area of one block is 2190 cm2, correct...
- 13N.2.sl.TZ0.2c: Assuming that no wood is wasted, show that the volume of wood required to make all 2600...
- 13N.2.sl.TZ0.2f: The blocks are to be painted. One litre of paint will cover \(22{\text{...
- 14M.1.sl.TZ1.8b: Calculate the volume of wood used to make the toy.
- 14M.2.sl.TZ1.6b: The volume of the lobster trap is 0.75 m3. Write down an...
- 17N.2.sl.TZ0.6f: Find the value of x.
- 17N.2.sl.TZ0.6e: Find the total cost of the ingredients of one special dessert.
- 17N.2.sl.TZ0.6d: Show that there is 20 cm3 of orange paste in each special dessert.
- 17N.2.sl.TZ0.6c: Find the cost of 100 cm3 of chocolate mousse.
- 17N.2.sl.TZ0.6b: Calculate the radius, r, of a hemisphere shaped glass.
- 17N.2.sl.TZ0.6a: Show that the volume of a cone shaped glass is 160 cm3, correct to 3...
- 15M.1.sl.TZ1.9b: Calculate the volume of the pyramid.
- 15M.1.sl.TZ1.15a: Find the value of a.
- 15M.1.sl.TZ1.5a: Calculate the volume of the Earth in km3. Give your answer in the...
- 15M.2.sl.TZ2.2c: Temi makes some crafts with perfume bottles, like the one above, once they are empty. Temi...
- 15M.2.sl.TZ2.2d: Temi covers the perfume bottles with a paint that costs 3 South African rand (ZAR) per...
- 15M.2.sl.TZ2.2a: (i) Show that the vertical height of the cone is 2.65 cm correct to three significant...
- 15M.2.sl.TZ2.2b: The bottle contains 125 cm3 of perfume. The bottle is not...
- 14N.2.sl.TZ0.3d: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped...
- 14N.2.sl.TZ0.3f: A company designs cone-shaped tents to resemble the traditional tepees. These cone-shaped...
- 14N.2.sl.TZ0.3a: Show that the slant height, l, is 5 m, correct to the nearest metre.