Solid built in sections whose heights form an AP: total volume
This type of question, asked 5 times: 18 Sep 2025 S1, 18 Sep 2025 S3, 19 Sep 2025 S2, 20 Sep 2025 S1, 22 Sep 2025 S3. All 5 questions below, oldest first.
Try each one first, then open its answer.
Question 1
18 Sep 2025 S1
65A decorative column is made in the shape of a regular hexagonal prism. The side length of its base is 10 cm. The column is built from multiple sections, and their heights form an arithmetic progression: the first section is 5 cm tall, and each subsequent section is 2 cm taller than the previous one. If the column has 4 sections in total, what is the total volume of the column?Tap an option to check your answer.
Question 2
18 Sep 2025 S3
65A cylindrical storage container has a base radius of 3 cm. It is designed with sections whose heights form an arithmetic progression, starting from 2 cm for the bottom section and reaching 10 cm for the topmost section, covering a total of 5 sections. What is the total volume of the container? (Use )Tap an option to check your answer.
Question 3
19 Sep 2025 S2
65A prism has an equilateral triangular base with a side length of 4 cm. Its height starts at 5 cm and increases by 1 cm for each subsequent layer, forming 5 layers in total. What is the total volume of the prism? (Use )Tap an option to check your answer.
Question 4
20 Sep 2025 S1
65A prism with a square base of side length 5 cm is constructed in layers. Its height follows an arithmetic progression, increasing from 4 cm in the first layer to 16 cm in the fourth layer. What is the total volume of the prism?Tap an option to check your answer.
Question 5
22 Sep 2025 S3
65The base of a prism is a rectangle whose length is twice its width. The perimeter of the base is cm. The prism's height decreases in an arithmetic progression from cm in the first layer to cm in the fourth layer. What is the total volume of the prism?Tap an option to check your answer.