A hemisphere sits perfectly on top of a cylinder to form a solid.
What is the volume of the solid?
- 1750 cm³
- 1950 cm³
- 2150 cm³
- 2350 cm³
Volume, SMB-016
The truncated cone, pictured below, is made by cutting a right cone of height 60 centimetres.
Find the volume of the truncated cone, giving your answer to the nearest cubic centimetre. (4 marks)
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Volume, SMB-015
A funnel is made in the shape of a square cone with radius 9.5 centimetres and height 19.5 centimetres.
Find the volume of the funnel in cubic centimetres, giving your answer correct to 2 decimal places. (2 marks)
Volume, SMB-014
The storage building below is constructed by joining a square pyramid to a cube, with all measurements in metres.
Find the volume of the solid in cubic metres. (3 marks)
Volume, SMB-013
The square pyramid below, has a side measurement of 120 metres and a perpendicular height `(h)` of 65 metres.
Find the volume of the pyramid in cubic metres. (2 marks)
Measurement, STD2 M1 2018 HSC 13 MC
A rectangular pyramid has base side lengths `3x` and `4x`. The perpendicular height of the pyramid is `2x`. All measurements are in metres.
What is the volume of the pyramid in cubic metres?
- `8x^3`
- `9x^3`
- `12x^3`
- `24x^3`
Measurement, STD2 M1 2017 HSC 30e
A solid is made up of a sphere sitting partially inside a cone.
The sphere, centre `O`, has a radius of 4 cm and sits 2 cm inside the cone. The solid has a total height of 15 cm. The solid and its cross-section are shown.
Using the formula `V=1/3 pi r^2h` where `r` is the radius of the cone's circular base and `h` is the perpendicular height of the cone, find the volume of the cone, correct to the nearest cm³? (3 marks)
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Show Worked Solution
`V = 1/3 xx text(base of cone × height)`
`text(Consider the circular base area of the cone,)`
`text(Find)\ x\ \ text{(using Pythagoras):}`
| `x^2` | `= 4^2-2^2 = 16-4 = 12` |
| `x` | `= sqrt12\ text(cm)` |
| `:. V` | `= 1/3 xx pi xx (sqrt12)^2 xx (15-6)` |
| `= 1/3 xx pi xx 12 xx 9` | |
| `= 113.097…` | |
| `= 113\ text{cm}^3\ text{(nearest cm}^3 text{)}` |
Measurement, STD2 M1 2015 HSC 8 MC
The Louvre Pyramid in Paris has a square base with side length 35 m and a perpendicular height of 22 m.
What is the volume of this pyramid, to the nearest m³?
- `257\ text(m)^3`
- `1027\ text(m)^3`
- `8983\ text(m)^3`
- `26\ 950\ text(m)^3`
Measurement, STD2 M1 2013 HSC 12 MC
A square pyramid fits exactly on top of a cube to form a solid.
What is the volume of the solid?
- 513 cm³
- 999 cm³
- 1242 cm³
- 1539 cm³