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Sectors and Area

This worksheet covers Sectors and Area, which is part of the Circles Destroyer module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Sectors and Area

Circles Destroyer • SAT Math Destroyer Crash Course

Set 3 — Mastery

A circular garden has a radius of $10$ meters. What is the area of a sector that subtends an angle of $60$ degrees at the center of the garden?

$rac{100 ext{ } ext{m}^{2}}{3}$

$rac{50 ext{ } ext{m}^{2}}{3}$

$rac{100 ext{ } ext{m}^{2}}{6}$

$rac{200 ext{ } ext{m}^{2}}{3}$

A pizza has a diameter of $12$ inches. If a slice represents a sector of $90$ degrees, what is the area of the slice?

$rac{36 ext{ } ext{in}^{2}}{ ext{}}$

$rac{12 ext{ } ext{in}^{2}}{ ext{}}$

$rac{18 ext{ } ext{in}^{2}}{ ext{}}$

$rac{24 ext{ } ext{in}^{2}}{ ext{}}$

If a circular track has a radius of $30$ meters, what is the area of a sector that corresponds to an angle of $120$ degrees?

$150 ext{ } ext{m}^{2}$

$100 ext{ } ext{m}^{2}$

$75 ext{ } ext{m}^{2}$

$180 ext{ } ext{m}^{2}$

A wheel of a bicycle has a radius of $0.5$ meters. What is the area of the sector formed by a $45$ degree rotation of the wheel?

$rac{1 ext{ } ext{m}^{2}}{8}$

$rac{1 ext{ } ext{m}^{2}}{4}$

$rac{1 ext{ } ext{m}^{2}}{16}$

$rac{1 ext{ } ext{m}^{2}}{2}$

A sector of a circle with a radius of $15$ cm has an area of $30 ext{ } ext{cm}^{2}$ . What is the angle of the sector in degrees?

$30$

$40$

$20$

$60$

A circular swimming pool has a radius of $7$ feet. If a section of the pool with a $150$ degree angle is drained, what is the area of the drained section?

$49 ext{ } ext{ft}^{2}$

$24.5 ext{ } ext{ft}^{2}$

$19.25 ext{ } ext{ft}^{2}$

$14.5 ext{ } ext{ft}^{2}$

A sector of a circle has a radius of $4$ cm and an area of $8 ext{ } ext{cm}^{2}$ . What is the angle of the sector in degrees?

$90$

$120$

$150$

$180$

What is the area of a sector with a radius of $5$ m and an angle of $72$ degrees?

$rac{25 ext{ } ext{m}^{2}}{3}$

$rac{50 ext{ } ext{m}^{2}}{3}$

$rac{25 ext{ } ext{m}^{2}}{6}$

$rac{100 ext{ } ext{m}^{2}}{6}$

A circular pizza is cut into slices, with one slice being a sector of $135$ degrees from a circle with a radius of $10$ inches. What is the area of that slice?