Ages 11–14🧮 Mathematics12 verified questions on this shelf
Angles in triangles (age 11+)
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
Try three questions
Tap an answer to check it. Every question and explanation was checked by independent verifiers that must agree.
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?
Keep going on this shelf
A free account keeps practising Angles in triangles (age 11+) with 12 verified questions, tracks the Skill as it blooms, and connects a real teacher when you want one. Every student account needs a parent's email first.