Mensuration

A square has an area of $64\text{ cm}^2$. What is its perimeter?

Calculate the area of a sector with radius $6\text{ cm}$ and angle $60^\circ$. Leave your answer in terms of $\pi$.

Find the perimeter of a semi-circle with radius $7\text{ cm}$. Take $\pi = \frac{22}{7}$.

The area of a rectangle is $60\text{ cm}^2$. If the width is $5\text{ cm}$, find the length.

Find the area of the kite shown in the diagram.

If the length of a rectangle increases by $20\%$ and the width decreases by $10\%$, what is the percentage change in area?

Calculate the area of an equilateral triangle with side length $10\text{ cm}$. Leave your answer in surd form.

The area of a ring (annulus) is $100\pi$ cm$^2$. If the width of the ring is $5$ cm, find the radius of the outer circle.

A wire of length $100$ cm is bent to form a sector of a circle with radius $r$. If the area of the sector is maximized, what is the value of the radius $r$?

In a square of side $10$ cm, a circle is inscribed. Then, a smaller square is inscribed in that circle. What is the area of the smaller square?

What is the volume of a cube whose total surface area is $24$ cm$^2$?

A cylinder has a base area of $25\pi$ cm$^2$ and a volume of $250\pi$ cm$^3$. What is its height?

The radius of a hemisphere is $3$ cm. Find its curved surface area. (Formula: $2\pi r^2$)

A triangular prism has a cross-sectional area of $15$ cm$^2$ and a length of $20$ cm. What is its volume?

A solid cylinder has a radius of $r$ and a height of $2r$. Find the ratio of its volume to the volume of a sphere with the same radius $r$.

The surface area of two spheres are in the ratio $1:4$. If the radius of the larger sphere is $10$ cm, what is the radius of the smaller sphere?

A sphere fits exactly inside a cube of side length $10$ cm, touching all six faces. Calculate the volume of the sphere in terms of $\pi$.

A sphere fits exactly inside a cylinder such that it touches the top, bottom, and the sides. What is the ratio of the volume of the sphere to the volume of the cylinder?

A swimming pool is in the shape of a prism with a trapezoidal cross-section. The pool is $20$ m long. The depth at the shallow end is $1$ m and the depth at the deep end is $3$ m. If the pool is $10$ m wide, calculate the total volume of water needed to fill the pool.

A solid metal cube of side length $6$ cm is melted and recast into a cylinder of height $8$ cm. Calculate the radius of the cylinder correct to 2 decimal places.

Find the area of a quadrant of a circle with a radius of $4$ cm.

A sector of a circle has a radius of $5$ cm and an arc length of $8$ cm. Calculate the area of the sector.

A pendulum of length $20$ cm swings through an angle of $15^{\circ}$. Find the distance traveled by the tip of the pendulum.

Find the length of the major arc if the minor arc of a circle with radius $7$ cm subtends $60^{\circ}$ at the center.

A sector of a circle with radius $9\text{ cm}$ has an arc length of $6\pi\text{ cm}$. Find the area of this sector in terms of $\pi$.

Find the length of the perimeter of a major sector with radius $12$ cm and central angle of the minor sector $60^{\circ}$.

A circular track has an inner radius of $20$ m and an outer radius of $25$ m. What is the area of a $40^{\circ}$ section of the track?

A square of side $10$ cm has a quarter-circle arc drawn from each of two opposite corners, meeting in the middle. Find the area of the overlapping region (the 'leaf' shape). (Use $\pi \approx 3.142$)

The diagram shows two concentric circles with radii $5$ cm and $12$ cm. A sector is defined by a central angle of $60^\circ$. Calculate the area of the region (annulus sector) between the two arcs.

A wire of length $20$ cm is bent into the shape of a sector of a circle with radius $r$. To maximize the area of the sector, what should the value of $r$ be?

1. Units of Measure: practice question 1 for Mensuration?

1. Units of Measure: practice question 2 for Mensuration?

1. Units of Measure: practice question 3 for Mensuration?

1. Units of Measure: practice question 4 for Mensuration?

1. Units of Measure: practice question 5 for Mensuration?

1. Units of Measure: practice question 6 for Mensuration?

1. Units of Measure: practice question 7 for Mensuration?

1. Units of Measure: practice question 8 for Mensuration?

1. Units of Measure: practice question 9 for Mensuration?

1. Units of Measure: practice question 10 for Mensuration?