Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
A first look
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Question 1 of 3
A student knows that the volume of any right prism is (area of its base) × height. To work out the volume of a right circular cylinder, they cut the circular base into many thin wedges, then rearrange the wedges so they look like a rectangle whose length is the circle’s circumference and whose width is the radius. Using this reasoning, which formula correctly gives the volume of the cylinder?
Question 2 of 3
A triangular wooden beam used as a support in a bookshelf has a right‑triangle cross‑section. The base of the triangle measures 8 cm and its vertical height measures 5 cm. The beam is 20 cm long. What is the volume of the beam in cubic centimeters?
Question 3 of 3
A cylindrical container has a radius of 3 cm and a height of 10 cm. Using the formula V = πr²h and approximating π as 3.14, what is the volume of the container?
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