A cuboid has the folg zwaal,j)b n)p2 53tnt) dyeow5hm3hnk5t92 lowing dimensions:length=9.6 cm,width=7.4 cm, and height=5.2hna35p3 j2 )5)t t olnadygkwz9)52th,mn web cm.
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 le4u(/zt 6y5/ 1c8c plovqaj imuather strips. The height of the baseball laying on the ground is 73 mm. Assuming the surface of 4mti q5ylo1/6 pucuvzc8aj/( 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 a cylindrical shap.brdn/40k+ayd cxzi4 v:yh( be. The diameter of the base of the tank va/ (:z dybr0b4dxink+.c yh4is 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 ona0we0b,b+igzb u1ji vt b8,*p a mountain range as a tourist attraction. The locations of the stops along the zipline can be desc,,e g+zji108a*pvu0wb ibbtbribed 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 tanks with goldfish inside. The first tank is in the s+whxp/ko)l ,c hape of a cylinder with diameter 4040 ck )/lwo+cx ,hpm and height 45 cm. The second tank is 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 showy4mw/6 8u ltzon in the diagram, has a base diameter of 0.40.4 m and a height of toyu/68 lmw4 z2.6 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 logs of let m *l5(ucgu-zngth 1.81.8 m and radius 9.29.2 cm mg lt(5uu-z*c. A wedge is cut from one log and the cross-section of this log is 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 and a slant hei*nx -l lpfz74 oerhmn*dh81,s ght of 3030 cme- 1n, *h*sxolfzr hmd np47l8. 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 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 mado4,z uixregux (/.e +qe in the form of a right circular cone that has volume (r,zx e4xq ugieou+/. $950 cm^3$ 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 ba0yunkz9w r;vtx98 5sts -n dr,se ABCD. The vertical height of the pyramid, VM, is 5 cm. Td99yusr w-x08tr ;v t,nnkz5 she sloping edges 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 7o;/zv:hr if s)jp7m i3.6 cm are used to construct a fence line. Part of the logs are removed, as illustratr;smo 7ihj3z :/v)f pied 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 wood1). 8 ( atx+tjcxbzm7em+k ezoen cabin. A wedge is cut from one log and the cross-section of this log is illustrated in the followinzm+mb txt x8azok1+ (ej7. )ecg 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 ea-wd+y9j li/ deliver their speciality birthday cakes. The box has a rectangular prism base, with a rectangular pyramid top, as illustrated in the diagram below with dimensi-9l+ ewjd/y aions 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 baseballmgq8zsfy*m * px8m4 +i3802wdz yuaav 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 thatg+a x/7eoy wrq3 n,corv u6;9y has a volumy nr6/,3oou ry+;qg7wxvac 9 ee 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 ABCD, with AB =3 cm. The vpr, 3xyui /7zpf5nxr0ertical heir7 fz/xu0p 5i3y ,pxnrght of the 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 the ha-e4 sa rm ocu(0es86left diagram below. The heig0h84aoau 6s (cm eesr-ht of the container 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. The volume of this cylinde8 ui+9as5b9u/of f oyyr is e fi o /958obya+usfu9yqual 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 (nn c 8ys 5vi,dc:cbl-cylinder. The pan has a diameter of 24 cm and a height of 5 c,l5cc dsi :8byn-nv( 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 hemisph8g2 0tz6wke ,sns8jjmkj k8y.ere (body), and a right cone (head). 86 kwmj s zge 8njskj,k8t02y.The robot is 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 spi ukwu:6t7ialq 3l,hw:nning top made up of a plastic cylinder and a plastic cone (tip)q k:l6 lwwuu 3a:iht,7.
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 t1admd(pc4 muxg:-)2a8o l ecbcur-.o rapezoid, ABCD, where AB is parallel to CD, AB uapacdx cd-4rcm:)o e.m1l2u(b8o - g=12 km and CD =8 km. The diagonal 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 pyramid has ujv/b.db.+c )kti abzo.s ,ae+32yho 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 midpoint of BC. uo . tvb3,a) bk+iea/oby.2h +cdj.szThe 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.  $cm^2$