Question
The diagram shows a sphcrical tank with radius 0.5 m and a cylindrical jug with diameter $24$cm and height $32$cm. The tank is full of water.
Calculate how many times the jug can be completely filled with water from the tank
[The volume, $V$, of a sphere with radius $r$ is $\frac43\pi r^3.]$
▶️Answer/Explanation
$36$
$V_{\text{sphere}} = \frac{4}{3}\pi r^3$
The radius of the tank is \( r = 0.5 \, \mathrm{m} = 50 \, \mathrm{cm}\).
$V_{\text{sphere}} = \frac{4}{3}\pi (50)^3$
$= \frac{4}{3}\pi (125000)$
$= \frac{500000}{3}\pi \, \mathrm{cm^3}$
The volume of a cylinder $V_{\text{jug}} = \pi r^2 h$
The diameter of the jug is \( 24 \, \mathrm{cm} \), so the radius is
$r = \frac{24}{2} = 12 \, \mathrm{cm}$
The height is \( h = 32 \, \mathrm{cm} \).
$V_{\text{jug}} = \pi (12)^2 (32)$
$= \pi (144)(32)$
$= 4608\pi \, \mathrm{cm^3}$
$\text{Number of fills} = \frac{V_{\text{sphere}}}{V_{\text{jug}}}$
$= \frac{\frac{500000}{3}\pi}{4608\pi}$
$\approx 36.17$
The jug can be completely filled 36 times from the full spherical tank
Question
The base of a cuboid measures l0cm by $7$cm.
The volume of the cuboid is 280 cm$^{3}$
Calculate the height of the cuboid.
▶️Answer/Explanation
$4$
- Base dimensions: 10 cm × 7 cm
- Volume: 280 cm³
$
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
$
$
280 = 10 \times 7 \times h
$
$
280 = 70h
$
$
h = \frac{280}{70}
$
$
h = 4 \, \text{cm}
$
Question
A circle has an area of $36\pi \rm{cm}^2$ .
(a) Find the circumference of the circle.
Give your answer in terms of $\pi $.
(b) The circle forms the base of a cylinder with height h cm.
The volume of the cylinder is $540\pi \rm{cm}^3$ .
Work out the value of h.
▶️Answer/Explanation
(a) $12\π$
(b) $15$
$
A = \pi r^2
$
$
36\pi = \pi r^2
$
$
36 = r^2
$
$
r = 6 \, \mathrm{cm}
$
circumference formula
$
C = 2\pi r
$
$
C = 2\pi(6)
$
$
C = 12\pi \, \mathrm{cm}
$
(b)
$
V = \pi r^2 h
$
$
540\pi = \pi(6^2)h
$
$
540\pi = \pi(36)h
$
$
540 = 36h
$
$
h = 15 \, \mathrm{cm}
$
Question
The diagram shows the net of a cuboid.
(a) Work out the surface area of this cuboid.
(b) Work out the volume of this cuboid.
▶️Answer/Explanation
(a) 220
(b) 200
From the diagram
Length (l) = 10 cm
Height (h) = 4 cm
Width (w) = 5 cm
$\text{Surface Area} = 2(lw + lh + wh)$
$= 2(10(5) + 10(4) + 5(4))$
$= 2(50 + 40 + 20)$
$= 2(110)$
$= 220 \text{ cm}^2$
(b)
$\text{Volume} = l \times w \times h$
$= 10 \times 5 \times 4$
$= 200 \text{ cm}^3$
Question
The total surface area of this cuboid is 369 cm2.
Work out the value of h.
▶️Answer/Explanation
Ans: 4.5
Total surface area of the cuboid: 369 cm²
Length (\( l \)): 15 cm
Width (\( w \)): 6 cm
Height (\( h \)): unknown (we need to find this)
$
\text{Surface Area} = 2(lw + lh + wh)
$
$
369 = 2(15(6) + 15(h) + 6(h))
$
$
369 = 2(90 + 15h + 6h)
$
$
369 = 2(90 + 21h)
$
$
369 = 180 + 42h
$
$
369 – 180 = 42h
$
$
h = \frac{189}{42}
$
$
h = 4.5 \, \text{cm}
$
Question
(a) The perimeter of a square is 28 mm.
Work out the length of one side of the square.
(b) Calculate the volume of a cylinder with radius 5.2 cm and height 15 cm.
Answer/Explanation
Ans:
(a) 7
(b) 1270 or 1274
or 1274.2 to 1274.4
Question
A cylinder has radius 3.6cm and height 16cm.
Calculate the volume of the cylinder.
Answer/Explanation
Ans: 651 to 652
Question
The diagram shows a cuboid.
The volume of this cuboid is 720cm3.
The width is 8cm and the length is 15cm.
Calculate h, the height of the cuboid.
Answer/Explanation
Ans: 6 cm
Question
A cuboid has volume 288cm3.
(a) The cuboid has length 12cm and width 5cm.
Calculate the height of the cuboid.
Answer/Explanation
Ans: 4.8 cm
(b) 1cm3 of the cuboid has a mass of 4g.
Work out the mass of the cuboid.
Answer/Explanation
Ans: 1152 g
Question
The volume, V, of a cylinder with radius r and height h is V = πr2h.
Calculate the volume of a cylinder with radius 7cm and height 8 cm
Answer/Explanation
Ans: 1230 or 1231 to 1232