Mathematics
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Fluidité · Pack B

9.2 Mensuration

Répondez à chaque question. Montrez les calculs si nécessaire.

Bronze

  1. A cuboid has length 10 cm, width 6 cm, height 3 cm. Find its volume.

  2. A cube has side 7 cm. Find its total surface area.

  3. A cylinder has radius 5 cm and height 8 cm. Find the volume in terms of π.

  4. A triangle base 6 cm, perpendicular height 8 cm. Find the area.

  5. A trapezium has parallel sides $a$ and $b$, height $h$. Find $A$ when $a = 4$, $b = 10$, $h = 5$.

  6. A square pyramid has base side 6 cm and height 9 cm. Find the volume.

  7. A cone has radius 6 cm, height 12 cm. Find the volume in terms of π.

  8. A sphere has radius 6 cm. Find the volume in terms of π.

  9. A cuboid with dimensions 6 × 4 × 3 cm. Find the surface area.

  10. A cylinder has radius 4 cm and height 10 cm. Find its total surface area in terms of π (including top and bottom).

Silver

  1. A triangular prism has triangular cross-section with legs 5 and 12 (right-angled), and length 20 cm. Find the volume.

  2. A square pyramid has base side 8 cm and slant height 10 cm. Find the surface area.

  3. A sphere has radius 6 cm. Find its surface area in terms of π.

  4. Make $h$ the subject of $V = \pi r^2 h$.

  5. A cone has volume $48\pi$ cm³ and radius 4 cm. Find its height.

  6. Find the volume of a cuboid pyramid (rectangular base) with base 6 × 4 and height 12.

  7. A cylinder has volume $200\pi$ cm³ and height 10 cm. Find its radius.

  8. A hemisphere has radius 5 cm. Find (a) volume, (b) curved surface area.

  9. A rectangular tank holds 1200 L of water. Length 2 m, width 1.5 m. Find the depth.

  10. Convert: a tank holds 250 L. Find its volume in (a) m³ and (b) cm³.

Gold

  1. A triangular prism has a right-angled triangular cross-section with legs 6 cm and 8 cm, and prism length 15 cm. Find its volume.

  2. A cuboid has square base side $x$ cm and height 3 cm, SA 80 cm². Find $x$.

  3. Rearrange $V = (1/3)\pi r^2 h$, then find $h$ when $V = 100$ cm³, $r = 5$.

  4. A solid metal sphere of radius 6 cm is melted and recast as a cylinder of radius 4 cm. Find the height.

  5. A cylinder open at the top has radius 3 cm and height 10 cm. Find the surface area (including base, no top).

  6. A cone has radius 6 cm and slant height 10 cm. Find the (a) curved surface area, (b) total SA.

  7. A cone has volume $48\pi$ cm³ and slant height 5 cm. Find the radius and height. (Hint: use Pythagoras for slant.)

  8. A composite shape: cylinder topped by a hemisphere. Cylinder r = 4, h = 10. Find total volume in terms of π.

  9. A cuboid has volume 360 cm³. Two sides are 6 and 5. Find the third.

  10. A swimming pool is a cuboid 25 m by 10 m by 2 m. Find (a) volume in m³, (b) capacity in litres.

Platinum

  1. A cone has radius 6 cm and height 12 cm. The top is sliced off parallel to the base, producing a smaller cone of radius 3 cm. Find the volume of the remaining frustum (in terms of π).

  2. A spherical balloon has volume $36\pi$ cm³. (a) Find the radius. (b) The balloon's radius doubles. By what factor does the volume increase?

  3. Make $r$ the subject of $V = (4/3)\pi r^3$.

  4. A skyscraper modelled as a cuboid is 154 m tall, 87 m wide, 30 m deep. (a) Find the glass area (4 vertical sides). (b) Find the space diagonal.

  5. A cylinder has radius $r$ and height $h$ where $h = 2r$. Volume = $54\pi$ cm³. Find $r$.

  6. A solid is formed by adding a cone to a cylinder. The cone and cylinder have the same radius 4 cm. The cylinder is 10 cm tall and the cone is 6 cm tall. Find the total volume.

  7. A hemispherical bowl has volume $\dfrac{2}{3}\pi r^3 = 250$ ml. Find $r$ (give 1 d.p.).

  8. Two cylinders are similar with linear scale factor 3. The smaller has volume 16 cm³. Find the larger volume.

  9. A pyramid has rectangular base 6 × 8 m and apex height 5 m above the centre of the base. Find the slant height to the midpoint of a long side.

  10. A cylinder of radius $r$ and height $h$ has surface area $A = 2\pi r^2 + 2\pi r h$. Make $h$ the subject.