A cuboid has the following dimensions:length=9.6 cm,widy q/-+ny2t zja);k:gy wpve-tt ny1+vth=7.4 cm, and height=5.2 cm.ttqyy vk:az- +y; -gt1)2y+j/p nevwn
1.Calculate the exact value of the volume of the cuboid, in $cm^3$.  $cm^3$
2.Write your answer to part (a) correct to
1.two decimal places;  
2.three significant figures.  
3.Write your answer to part (b) (ii) in the form $a\times10^k$, where $1 \leq a \lt 10$
and $k \in \mathbb{Z}$  $\times 10^2$

  The surface area of a ekej0i47i-al )bk )w2l 2ehd 0wkc2do baseball is made up of two equal leather strips. The height of the baseball laying on the ground is 73 mm. Assuming the surface of the0ii)hwwo kjc)7la-e2d 4 e2kk2dl0be baseball is a sphere:
1.Find the area of one leather strip used to make the baseball in $mm^2$. Give your answer correct to one decimal place.  $mm^2$
2.Find the circumference of the baseball. Give your answer in mm correct to three significant figures.  mm

  A water storage tank has a cylindrica jaf;9.5p 2dma*4h sd8eequpyl shape. The diameter of the base of the tank q4ap f2p u.9a ;em8jyh*dd5esis 0.5680.568 m. The height of the tank is 0.8550.855 m. This is shown in the following diagram.




1.Write down the radius, in m, of the base of the tank.  m
2.Calculate the area of the base of the tank.  $m^2$
George is going to paint the curved surface and the base of the water storage tank.
3.Calculate the area to be painted.  $m^2$

  A zipline is installed on a mountain range avajwcl69b o; u 94o kzl+t yv 5kor*3cbh/s)1qs a tourist attraction. The locations of the stops along j;b aoq volocz6k15ruc k9)*sltywbh3+4/ v9the zipline can be described by coordinates (in metres) in reference to the xx, yy, and zz-axes, where the xx and yy axes are in the horizontal plane and zz-axis is in the vertical plane.
Stop G, at ground level, has coordinates (1000,20,0)(1000,20,0). Stop, T, located near the top of the mountain, has coordinates (10,15,550)(10,15,550).


1.Find the distance between stops G and T, rounding your answer to the nearest metre.  m
A new stop, M, is built exactly half-way between stops G and T.
2.Find the coordinates of stop M.(  ,  ,  )
3.Write down the height of stop M, in metres, above the ground.  

  Peter has two water y*k4qbv 89 p0k6khxi;.-m o k tj5lsrytanks with goldfish inside. The first tank is in the shape of a cylinder with diameter 4040 cm and height 45 cm. The second tank is in the shape of a cuboid with length 40 cm, l m9486vkk-kx.*h pt5sj;ob0kqry y iwidth 32 cm, and height 42 cm.

1.Calculate the volume, giving your answer in $cm^3$ correct to three significant figures,
1.of the first water tank;  $cm^3$
2.of the second water tank.  $cm^3$
Each goldfish requires $15000 cm^3$ of fresh water for a comfortable life.
2.Calculate the number of goldfish Peter can safely put into his tanks.  goldfish

  A right cylinder, as shown in the diagram, has a base diameter of 0.40,f bztobn py 87 7b r0fb0mf4rxw0e1a3.4 m and a heigb,t 1r e0w7fn0f7py8fb 03ab4rox bmzht of 2.6 m.

1.Write down the radius, in cm, of the base of the cylinder.  cm
2.Calculate the area, in $m^2$, of the base of the cylinder.  $m^2$
3.Calculate the area, in $m^2$, of the curved surface of the cylinder.  $m^2$

  John is building furniture using cylindrical logsk;jrjme 2 :a-fwsc 22r of length 1.81.8 m and radius 9.29.2 cm. A wedge is cut from one log and the cross-section of this log is;sfjmj -we 22 ka:2crr illustrated in the following diagram.

1.Find the length of the wedge arc, ABC.  cm
2.Find the area of the empty sector, OABC.  $cm^2$
3.Find the volume of each log.  $cm^3$

  A solid right circular cone has a base radius of 1818 cm andk3.1dp iwko3o a slant height of 3030 cm. A smaller right circula1wi3 o pkdo3.kr cone, with a vertical height of 88 cm and a slant height of 1010 cm, is removed from the top of the larger cone, as shown in the diagram.


1.Calculate the radius of the base of the cone which has been removed.  cm
2.Calculate the curved surface area of the cone which has been removed.  $cm^2$
3.Calculate the curved surface area of the remaining solid.  $cm^2$

  A birthday party cap is made in the form of a riibhpb -z3 b;kvs0q kwe8g5.*ap:4 tulght circular cone that has voluma5uk*;4q i0s3zvp bkb -b8ht l:wp.e ge $950 cm^3$ and vertical height 20 cm.



1.Find the radius, rr, of the circular base of the cone.  cm
2.Find the slant height, ll, of the cone.  cm
3.Find the curved surface area of the cone.  $cm^2$

  A right pyramid has apex V and square base eddj*).croyej c rih6x) ibq77g,+4 gABCD. The vertical height of the pyramid, VM, is 5 cm. The sloping edgdo7qi e * ic6)r.rjgyb h)xcdgje,+ 47es are 8 cm long.



1.Calculate the length of MC.  cm
2.Calculate the size of the angle that sloping edge VC makes with the
vertical height of the pyramid.  $^{\circ}$
3.Calculate the area of the triangle ABC.  $cm^2$

  Cylindrical logs of length 2.2 m and radius 7.6 cm are usedp9mmymwr;9 * a to construct a fence line. Part of tp m;a mw*9mr9yhe logs are removed, as illustrated in the diagram below.


Find the volume of each log.  $cm^3$

  Cylindrical logs of length 2.7 m and radius 7.5cm are used to buildiusw/qp745n7 jak0zvvg 9(wd a wooden cabin. A9zqgadjwps /7kv5vu w 4(i0 7n wedge is cut from one log and the cross-section of this log is illustrated in the following diagram.


1.Convert 108 degrees into radians, leaving your answer in exact values.
2.Find the length of the missing arc ABC.  cm
3.Find the area of the missing sector ABCO.  $cm^2$
4.Find the volume of this log.  $cm^3$

  A bakery has designed a box to deliver their speciality birthday cakes. Thex kum o-my23+p box has a rectangular prism base, with a rectangular pyramid okm-pu2mx3 y+top, as illustrated in the diagram below with dimensions shown.
After the cake is put into the box, the outside of the box is completely wrapped in colourful gift paper.


Point O shown on the diagram is the midpoint of the base of the pyramid.
1.Find the value of a shown in the diagram; the slant height of one of the pyramid faces.  cm
2.Find the total outer surface area of the box to be wrapped in gift paper.  $cm^2$

  The height of a basebal/ 0t4f xogjpp:l laying on the ground is 73 mm.
1.Assuming that the baseball is a perfect sphere, calculate its volume in $mm^3$.Give your answer in the form $a\times 10^k$, where $1 \leq a \lt10$ and $k \in \mathbb Z$,correct to three significant figures.  $\times10^5\: mm^3$
The volume of a volleyball is $4.64 \times 10^6 mm^3$.
2.Calculate how many times greater the volume of the volleyball is when compared to the baseball. Give your answer correct to the nearest whole number.  

  An ice cream cup is designed in the form of a right circular cone thatxj26/zpk / nti has a volume nzpx 6tk2i/j/ of $150 cm^3$ and a vertical height of 14 cm.


1.Find the radius, r, of the circular base of the cone.  cm
2.Find the slant height, l, of the cone.  cm
3.Find the curved surface area of the cone.  $cm^2$

  A right pyramid has apex V and squarexq6*r7te )rd8-ev xns base ABCD, with AB =3 cm. The vertical height of the pyramid, VM,s7x86 r dt er-veqnx)* is 12 cm.


1.Calculate the length of VA.  cm
2.Calculate the volume of the pyramid.  $cm^3$

  A container has the shape of a right circular cylwco9o2,btsk 3inder, as shown in the left diagram below. The height of the contai 9o3 b2,ctkowsner is 5 cm, and the diameter of the cylinder's base is 8 cm.


1.Find the volume of the container, V.  $cm^3$
A cup full of water has the shape of hemisphere, as shown in the right diagram above. The water from the cup is poured into the container and fills one third of the container.
2.Find the radius of the cup, r.  cm

  A right cylinder has height hh mm and diameter xx mm.s,-fbktu 4 jynp4w33gcj :6ht The volume of this cylinder is equal gb634t 4kfj,sy u:wcn hp3 t-jto $45mm^3$.


The total surface area, A, of the cylinder can be expressed as $A = \frac{\pi}{2}x^2 + \frac{k}{x}$.
1.Find the value of k.k=  
2.Find the value of x that makes the total surface area a minimum.x=  mm

  A loaf pan is made in the so94wfr:hq lge * 6s*.ecpl7nmdq2e .:bpij 9jhape of a cylinder. The pan has a diameter of 24 cm and a heenw.p je q9i:2m4r 6h:ql*bs7e*.g9 ljcofpd ight of 5 m.


1.Calculate the volume of this pan.  $cm^3$

Gloria prepares enough bread dough to exactly fill the pan. The dough was in the shape of a sphere.

2.Find the radius of the sphere in cm, correct to one decimal place.  cm

The bread was cooked in a hot oven. Once taken out of the oven, the bread was left in the kitchen.
The temperature, T, of the bread, in degrees Celsius,$^{circ}C$, can be modelled by the function
$T(t)=a\times(1.51)^{-\frac{t}{3}}+21,t\geq0$
where a is a constant and tt is the time, in minutes, since the bread was taken out of the oven.
When the bread was taken out of the oven its temperature was 205$^{\circ}C$.
3.Find the value of a.  
4.Find the temperature that the bread will be 10 minutes after it is taken out of the oven.
The bread can be eaten once its temperature drops to 35$^{\circ}C$.  $^{\circ}C
5.Calculate, to the nearest minute, the time since the bread was taken out
of the oven until it can be eaten.  minutes
6.In the context of this model, state what the value of 21 represents.

  A toy robot has four main parts: two cylinders (legs), a h 3be215nf sze:k8 ifucemisphere (body), and a right cone (head). The robot is represented nzf3: e28if5ku1 cseb by the diagram below.
The legs have heights of 10 cm and volume $80 cm^3$ each.
The hemisphere has a diameter 30 cm.
The cone has a radius 5 cm.
The toy robot's total height is 32 cm.


1.Calculate the distance between the robot's legs.  cm
2.Calculate the volume of the hemisphere, correct to the nearest $cm^3$.  $cm^3$
3.Calculate the volume of the cone.  $cm^3$
4.Calculate the total surface area of the toy robot. Give your answer to the nearest $cm^2$.  $cm^2$

  The following diagram shows a toy spinning top mad + s.*gspqj6yke up of a plastic cylinder and a plastig +.qy6pk jss*c cone (tip).
The diameter of the cylinder is 0.6 cm.
The height of the cylinder is 2.5 cm.
The radius of the base of the cone is 2 cm.
The slant height of the cone is 2.8 cm.


1. 1.Calculate the vertical height of the cone, in cm. Give your answer correct to thee significant figures.  cm
2.Use your answer from the part (i) to calculate the total volume of the spinning top. Give your answer correct to two decimal places.  $cm^3$
One spinning top was deemed as defected after the manufacturing process due to insufficient amount of plastic. As a result, the stem was shorter than usual.
2.Find the height of this short stem, given that the amount of plastic used for this spinning top was $8.5 cm^3$.
The paint used for colouring the toy has layer thickness of 0.04 cm.  cm
3.Calculate the total surface area of a non-defective spinning top.  $cm^2$
4.Calculate the volume of paint needed to dye 1000 non-defective spinning top's. Give your answer correct to one decimal place.  $cm^3$

  A large plot of land is shaped like a tdhtfy k,*1p)wrapezoid, ABCD, where AB is parallel to CD, AB =12 km and CD =8 km. The diagonal BD of the trapezoid is equafwpy,*kd th) 1l to 10km. The internal angle $\mathrm{A}\hat{\mathrm{B}}\mathrm{D}$ is equal to 58$^{circ}$.


Let a new point, H, be a point on AB closest to D.
1.Calculate the distance from H to D.  km
2.Calculate the length of AD.  km
3.Calculate the size of the angle $\mathrm{D}\hat{\mathrm{A}}\mathrm{B}$.  $^{circ}$
A landowner estimates that the length of AD is equal to 11.5 km.
4.Calculate the percentage error in the landowner's estimate.  %

The landowner decides to install cone-shaped concrete bollards along the perimeter of the plot of land. The bollards are to be installed at a distance of 100 m from each other. The radius of the base of each bollard is 20 cm and the height of each bollard is 40 cm.

5.Calculate the volume of one of the bollards.  $cm^3$
6.Calculate the total volume of concrete needed to install all the bollards.  $cm^3$

  A plastic toy is in the shape of a rightfd66gt* 2t*zo hwip 3s pyramid. The pyramid has a square base with the sides 4 cm long. The diagram below represents this pyramid, labelled VABCD. V is the vertex of the pyramid. O is the center of the base ABCD. M is the mi6w6pttid3z*sgfo h2* dpoint of BC. The angle $\mathrm{V}\hat{\mathrm{B}}\mathrm{C}$ is equal to$75^{circ}C$.


1.Calculate the length of VM.  cm
2.Calculate the height of the pyramid, VO.  cm
3.Find the volume of the pyramid, in $cm^3$. Give your answer correct to one decimal place.  $cm^3$
4.Write down your answer to part (c) in the form $a \times 10^k$, where $1 \leq a \leq 10$ and $k \in \mathbb Z$.  $\times10^1\:cm^3$

Another plastic toy is in the shape of a right cone. The height of the cone is equal to the height of the pyramid, and the diameter of the cone's base is equal to 4 cm.

5.Determine whether the amount of plastic used to manufacture the pyramid is also enough to manufacture this cone.  $cm^3$

After heating, the pyramid deforms in such a way that the angle $\mathrm{V}\hat{\mathrm{B}}\mathrm{C}$ decreases by 20%. The side VC decreases in length during this deformation, however sides VB and BC stay the same length.

6.Calculate
1.The new distance from the pyramid vertex V to point M.  cm
2.The new area of the pyramid's side VBC.  $cm^2$