Area and Volume：練習問題

A solid right circular cylinder has a base radius of \(3\text{ cm}\) and a height of \(14\text{ cm}\). Find the curved surface area of the cylinder. (Take \(\pi = \frac{22}{7}\))

A right pyramid has a square base with a side length of \(9 \text{ cm}\). If the perpendicular height of the pyramid is \(10 \text{ cm}\), find its volume.

A solid metal cube with a side length of \(6 \text{ cm}\) is melted down and recast into a solid right circular cylinder with a base radius of \(3 \text{ cm}\). Find the height of the cylinder correct to 2 decimal places. (Take \(\pi \approx 3.14159\))

Calculate the total surface area of a rectangular prism (cuboid) with length \(10 \text{ cm}\), width \(3 \text{ cm}\), and height \(5 \text{ cm}\).

A paper sector of a circle with a radius of \(9 \text{ cm}\) and a central angle of \(120^\circ\) is folded to form the curved surface of a right circular cone. Find the base radius of the cone.

A right prism has a height of \(15\text{ cm}\). If the base of the prism is a square with a side length of \(4\text{ cm}\), calculate the volume of the prism.

A metal right circular cylinder with base radius \(6 \text{ cm}\) and height \(10 \text{ cm}\) is melted down and recast into a solid right pyramid with a square base of side length \(6 \text{ cm}\). Find the height of the pyramid. (Take \(\pi = 3\))

A frustum of a right circular cone has a base radius of \(6\) cm, a top radius of \(3\) cm, and a perpendicular height of \(4\) cm. Calculate its volume in terms of \(\pi\).

A rectangular swimming pool has a length of \( 25 \text{ m} \) and a width of \( 10 \text{ m} \). The pool is filled with water to a uniform depth of \( 2 \text{ m} \).

(a) Calculate the volume of water in the pool in cubic meters (\( \text{m}^3 \)).
(b) Find the total surface area of the interior of the pool (the bottom and the four side walls) that is in contact with the water.

A right circular cone and a hemisphere share a common circular base with a radius of \( 6 \text{ cm} \). The vertical height of the cone is \( 8 \text{ cm} \).

(a) Find the slant height of the cone.
(b) Calculate the total volume of the composite solid in terms of \( \pi \).
(c) Calculate the total surface area of the exterior of the solid in terms of \( \pi \).