Circles, Cones, Cylinders (Perimeter, Area, Volume)：練習問題

What is the area of a circle with a radius of \( 5 \text{ cm} \)? (Take \( \pi = 3.14 \))

Which of the following statements about the cross-sections of a solid right circular cylinder is correct?

A solid right circular cylinder has a base radius of \( 5 \text{ cm} \) and a height of \( 12 \text{ cm} \). A conical hole is drilled into the cylinder such that the cone's base matches the cylinder's top face and its vertex reaches the center of the bottom base. If the slant height of the cone is \( 13 \text{ cm} \), find the total surface area of the remaining solid in terms of \( \pi \).

A solid right circular cylinder is cut by a plane parallel to its base. What is the shape of the resulting cross-section?

A circular pond has a circumference of $$88 \text{ meters}$$. What is the area of the pond? Use $$\pi = \frac{22}{7}$$.

If a circle has a radius of \( 13 \text{ cm} \), what is the length of its diameter in centimetres?

A running track is formed by a rectangle of length \(50 \text{ m}\) and width \(28 \text{ m}\), with two identical semicircles attached to its shorter sides. Calculate the total area of the track in square metres. (Take \( \pi = \frac{22}{7} \))

A solid object is formed by joining a right circular cylinder and a right circular cone at their common circular base with radius \( r \). The cylinder has a height of \( 10 \) cm. The volume of the cone is exactly \( \frac{1}{5} \) of the volume of the cylinder. If the total volume of the composite solid is \( 1848 \) cm\(^3\), calculate the total height of the object. (Take \( \pi = \frac{22}{7} \))

A closed cylindrical storage container has a radius ( \(R\) ) of \(7 \text{ cm}\) and a height ( \(H\) ) of \(10 \text{ cm}\) . Use \(\pi = \frac{22}{7}\) .

a) Calculate the area of the circular base of the container in square centimeters ( \(\text{cm}^2\) ).

b) Calculate the volume ( \(V\) ) of the container in cubic centimeters ( \(\text{cm}^3\) ).

c) Calculate the area of the curved lateral surface ( \(A_L\) ) of the container in square centimeters ( \(\text{cm}^2\) ).

A construction company uses a large right circular conical tank to hold cement powder. The tank has a radius \(R = 6 \text{ meters}\) and a height \(H = 10 \text{ meters}\). Use \(\pi = 3.14\).

a) Calculate the volume of the conical tank in cubic meters (\(\text{m}^3\)).

b) The cement is transferred into small cylindrical barrels. Each barrel has a radius of \(1 \text{ meter}\) and a height of \(2 \text{ meters}\). Calculate the volume of one cylindrical barrel in \(\text{m}^3\).

c) Assuming no waste, how many complete cylindrical barrels can be filled from the conical tank?