The area `(A)` of a circle is given by the formula `A=\pi r^2`, where `r` is the radius.
What is the value of `A`, correct to three significant figures, if `r=3.55` ?
- 39.5
- 39.6
- 39.591
- 39.592
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The area `(A)` of a circle is given by the formula `A=\pi r^2`, where `r` is the radius.
What is the value of `A`, correct to three significant figures, if `r=3.55` ?
`B`
`A` | `=pi\r^2` | |
`=pi xx3.55^2` | ||
`=39.591…` | ||
`=39.6\ \ text{(3 sig fig)}` |
`=>B`
The diagram shows a sector with an angle of 120° cut from a circle with radius 10 m.
What is the perimeter of the sector? Write your answer correct to 1 decimal place. (3 marks)
`40.9\ \ (text(1 d. p.))`
`text(Arc length)` | `= 120/360 xx 2 xx pi xx 10` |
`= 20.94` |
`:.\ text(Perimeter)` | `= 20.94 + 2 xx 10` |
`= 40.94` | |
`= 40.9\ \ (text(1 d. p.))` |
The diagram shows a shape made up of a square of side length 8 cm and a semicircle.
Find the area of the shape to the nearest square centimetre. (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
`89\ text(cm² (nearest cm²))`
`text(Area)` | `=\ text(Area of square + Area of semicircle)` |
`= 8 xx 8 + 1/2 xx pi xx 4^2` | |
`= 89.13…` | |
`= 89\ text(cm² (nearest cm²))` |
A shape consisting of a quadrant and a right-angled triangle is shown.
What is the perimeter of this shape, correct to one decimal place?
`text(B)`
`text(Using Pythagoras to find radius)\ (r):`
`r` | `= sqrt(10^2 – 6^2)` |
`= sqrt64` | |
`= 8\ text(cm)` |
`text(Arc length)` | `= 1/4 xx 2 pi r` |
`= 1/4 xx 2 xx pi xx 8` | |
`= 12.56…\ text(cm)` |
`:.\ text(Perimeter)` | `= 8 + 6 + 10 + 12.56…` |
`= 36.57…` |
`=>\ text(B)`
In the circle, centre `O`, the area of the quadrant is 100 cm².
What is the arc length `l`, correct to one decimal place?
`C`
`text(Find)\ r:`
`text(Area)` | `= 1/4 pir^2` |
`100` | `= 1/4 pir^2` |
`r^2` | `= 400/pi` |
`:. r` | `= 11.283…\ text(cm)` |
`text(Arc length)` | `= theta/360 xx 2pir` |
`= 90/360 xx 2pi xx 11.283…` | |
`= 17.724…` | |
`= 17.7\ text(cm)` |
`=> C`
The diagram shows the floor of a shower. The drain in the floor is a circle with a diameter of 10 cm.
What is the area of the shower floor, excluding the drain?
`B`
`text(Area)` | `=\ text(Square – Circle)` |
`= (100 xx 100)-(pi xx 5^2)` | |
`= 10\ 000-78.5398…` | |
`= 9921.46…\ text(cm²)` |
`=> B`
What is the area of the shaded part of this quadrant, to the nearest square centimetre?
`B`
`text(Area)` | `=\ text(Area of Sector – Area of triangle)` |
`= (theta/360 xx pi r^2)-(1/2 xx bh)` | |
`= (90/360 xx pi xx 8^2)-(1/2 xx 4 xx 4)` | |
`= 50.2654…-8` | |
`= 42.265…\ text(cm²)` |
`=> B`
The sector shown has a radius of 13 cm and an angle of 230°.
What is the perimeter of the sector to the nearest centimetre? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
`text(78 cm)\ \ \ \ text((nearest cm))`
`text(Perimeter)` | `= 2 xx text(radius) + text(arc length)` |
`text(Arc length)` | `= theta/360 xx 2 xx pi xx r` |
`= 230/360 xx 2 xx pi xx 13` | |
`= 52.1853…` | |
`:.\ text(Perimeter)` | `= 2 xx 13 + 52.1853…` |
`= 78.1853…` | |
`=text(78 cm)\ \ \ \ text((nearest cm))` |