A cuboid has the following dimensions:length=9.6 cm,width=7.4 cm,bg ds+ jb* 0qd++--jb bj74h jc,mzwt-l 5fwgh and height=5.2 twcl +qshj+w*h+5-g jz4 bg7-f,jbb0 d-bmjdcm.
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 baseball is made up of two equal leather strips. The heighnt:h9*unwa8*h*k6p ebu; ir et of the baseball laying on the ghhunber ten** ;p6k9:8a wiu*round is 73 mm. Assuming the surface of the 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 iea58a2sz **p+rf 9mls-vbr wa cylindrical shape. The diameter of the base of the tank is 0.5680.568 m. The height of the tank is+irvpl 2*8mzf9 wa5e-* sa rbs 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 as a tourist attraction 08jjaxyn:ct 8. The locations of the stops along the zipline can be described by coordinates (in metres) in reference to the xx, yy, and zz-axes, where the xx anj jt 08xc:8nayd 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 tanks with goldfish inside. The fitu88w;w0 y2tqr 6kvkjrst tank is in the shape of a cylinder with diameter 4040 cm and height 45 cm. The second tank tvtq;yur82 w 6 jk8wk0is in the shape of a cuboid with length 40 cm, width 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 ba ,i,f3kq 0ax k6cimncl4ko98pse diameter of 0.40.4 m and a height of8k3 6kncom90i cxf,kal 4ip,q 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 cylinm:-poqo8bzl y8 , wjtm:s h,.mdrical logs 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 illustrated in the following diomth - 8: pqyls.,8j,zbwom m:agram.

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 radi81juwv 02g mbpus of 1818 cm and a slant height of 3030 cm. A smaller right circular cone, with a vertical height of 88 cm and a slant height of 1010 cm, is removed from the top of the larbgwv m0p2j 8u1ger 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 right circular cone that cdiy+l37nyn6 has volumeycn36yn+di7l $950 cm^3$ 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 ewih he d2mq9.8 (u5ifk74uumV and square base ABCD. The vertical height of the pyramid, VM, is 5 cm. The sloping edges7.wi8uhm4meuf2 9h dk(5ei qu 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 used to construct a fen. qjnc3sxiqzu5(/p*9w 5hnjr3exqe, ce line. Part of the logs are removehr*/ 5 eji3.zqq uc ,snejp3xxn9(w5qd, 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 build a q 7/ezhd*a3lr wooden cabin. A wedge is cut from one log and the cross-section of this log isrq*7la /dze h3 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 t*:-m6dx pyvo aheir speciality birthday cakes. The box has a rectangular prism base, with a rectangular pyramid top, as illustratedda*px6v- myo: 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 baseball laying onp:ayk8ri/ d l. 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 that fjrx1/cc *v3t has a volum3/ rc*1xjvftce 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 square base o fw*q*v.uo* mABCD, with AB =3 cm. The vertical height of thw* ov**fuqm.oe pyramid, VM, 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 cylinder, as shown in t;--y33dxa1pphliz b/ nk w9 hm, zkw0nhe left diagram below. The height of the container is 5 cm, and the diai1/-nkkxm-3 z0b,; lyww 9n3hpzadp hmeter 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 bhie fmja3yv2zj* a7m3(s.c3. The volume of this cylinder is equzaish 3(bj. a*jfyc37m2mev3 al to $45mm^3$.


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 shape of a cylinder. The pan has a 3 ,fl-3wtd vx/cohhm(ypdy 35diameter of 24 cm and a height h5c(y-h3pt3dm l,/yfxv3 odw 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) *c-.ronzqt+5-m1w5k xwjwo r , a hemisphere (body), and a right cone (head). The robot is xjnr t *kmc5wo1wz5+-qor.w-represented 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 /pvvyp g1b. l5hq8l 9ytop made up of a plastic cylinder and a plastic cobvy.p/y v1589p llgqhne (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 sha* 1xch .mb5)k8devdkm ped like a trapezoid, ABCD, where AB is parallel to CD, AB =12 km and CD =8 km. The diagonadhm cxe)1mv 5.kk 8*dbl BD of the trapezoid is equal 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 right pyramid. The pyr83 3fyzrm9f)mgh qeqt)z-; q5 rh8 mbfamid has a square base with the sideqq 3rf5 -ytzqh )8mfmm e;9b hzf3gr8)s 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 midpoint 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.  $cm^2$