Question:
How many paper cups (of the dimensions shown below) can be made from one A4 paper?
How many paper cups (of the dimensions shown below) can be made from one A4 paper?
Show Hint
For frustum-based problems, include both lateral and base areas if required. Compare the total material available with the required area for clarity.
Updated On: Jan 4, 2026
Hide Solution
Verified By Collegedunia
Solution and Explanation
Step 1: Determine the dimensions of the paper cup.
- The paper cup has a frustum shape with a height of \(6.5 \, \text{cm}\), top diameter \(6.5 \, \text{cm}\), and bottom diameter \(5.5 \, \text{cm}\).
Step 2: Calculate the lateral surface area of one cup.
The lateral surface area of a frustum is given by: \[ \text{Lateral Area} = \pi (r_1 + r_2) \cdot l, \] where \(r_1 = 3.25 \, \text{cm}\), \(r_2 = 2.75 \, \text{cm}\), and \(l = \sqrt{(6.5)^2 + (3.25 - 2.75)^2} \approx 6.52 \, \text{cm}\).
Substituting values: \[ \text{Lateral Area} = \pi (3.25 + 2.75) \cdot 6.52 \approx 125.4 \, \text{cm}^2. \]
Step 3: Compare with the area of an A4 paper.
The total area of A4 paper is \(21 \, \text{cm} \times 29.7 \, \text{cm} = 623.7 \, \text{cm}^2.\)
Step 4: Calculate the number of cups.
Each cup requires \(125.4 \, \text{cm}^2\). The number of cups that can be made is: \[ \text{Number of cups} = \frac{623.7}{125.4} \approx 3. \]
- The paper cup has a frustum shape with a height of \(6.5 \, \text{cm}\), top diameter \(6.5 \, \text{cm}\), and bottom diameter \(5.5 \, \text{cm}\).
Step 2: Calculate the lateral surface area of one cup.
The lateral surface area of a frustum is given by: \[ \text{Lateral Area} = \pi (r_1 + r_2) \cdot l, \] where \(r_1 = 3.25 \, \text{cm}\), \(r_2 = 2.75 \, \text{cm}\), and \(l = \sqrt{(6.5)^2 + (3.25 - 2.75)^2} \approx 6.52 \, \text{cm}\).
Substituting values: \[ \text{Lateral Area} = \pi (3.25 + 2.75) \cdot 6.52 \approx 125.4 \, \text{cm}^2. \]
Step 3: Compare with the area of an A4 paper.
The total area of A4 paper is \(21 \, \text{cm} \times 29.7 \, \text{cm} = 623.7 \, \text{cm}^2.\)
Step 4: Calculate the number of cups.
Each cup requires \(125.4 \, \text{cm}^2\). The number of cups that can be made is: \[ \text{Number of cups} = \frac{623.7}{125.4} \approx 3. \]
Was this answer helpful?
1
0
Top Questions on Geometry
- If \[ \lim_{x \to 0} \frac{e^{a(x-1)} + 2\cos(bx) + e^{-x}(c - 1)}{x \cos x - \ln(1 + x)} = 2, \] Then the value of \( a^2 + b^2 + c^2 \) is:
- If \( P(10, 2\sqrt{15}) \) lies on the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and the length of the latus rectum is 8, then the square of the area of \( \Delta PS_1S_2 \) is [where \( S_1 \) and \( S_2 \) are the foci of the hyperbola].
- If \( \cos(\alpha + \beta) = -\frac{1}{10} \) and \( \sin(\alpha - \beta) = \frac{3}{8} \), where \[ 0<\alpha<\frac{\pi}{3} \quad \text{and} \quad 0<\beta<\frac{\pi}{4}, \] and \[ \tan(2\alpha) = \frac{3\left(1 - \sqrt{55}\right)}{\sqrt{11} \left(s + \sqrt{5}\right)}, \] and \( r, s \in \mathbb{N} \), then \( r^2 + s \) is:
- If \( O \) is the vertex of the parabola \( x^2 = 4y \), \( Q \) is a point on the parabola. If \( C \) is the locus of a point which divides \( OQ \) in the ratio \( 2:3 \), then the equation of the chord of \( C \) which is bisected at the point \( (1,2) \) is:
- The locus of the point of intersection of tangents drawn to the circle \[ (x - 2)^2 + (y - 3)^2 = 16, \] which subtends an angle of \(120^\circ\), is:
View More Questions
Questions Asked in CEED exam
- Creativity: Mandatory question (20 marks) In the given frames, sketch a story by incorporating the symbols shown. Give an appropriate title to the story. Use \textbf{ANY TWO symbols in each frame, and use each symbol ONLY ONCE in the whole story. Symbols may be rotated, flipped, or scaled proportionately. Additional elements may be drawn to make the story meaningful. Label the frames 1, 2, 3, and 4 in the bottom-left corners.}
- CEED - 2026
- Sketching and Drawing
- Form Sensitivity: Mandatory question (20 marks) Conceptualise and render a usable single-seat furniture inspired by a sphere for a living room. The sphere may be modified by cutting, adding, subtracting, deforming, or repeating; however, the essence of the sphere should be retained.
- CEED - 2026
- Sketching and Drawing
- Visual Sensitivity: Mandatory question (20 marks = 4 × 5 marks) A new museum with the theme “Indian Museum of Science†is being set up, which will cater primarily to Indian visitors. Create four icons based on the museum theme to communicate the following sections to visitors: Robotics, Energy Science, Ocean Science, and Food Technology. Icons should use only visuals (no text), be drawn in black and white, and maintain a consistent visual language.
- CEED - 2026
- Animation
- Problem Identification: Mandatory question (20 marks) An elderly couple from Srinagar is travelling to Chennai for medical treatment. They will travel by train for most of their journey and plan to take a bus and auto rickshaws for all local commutes. Imagine their journey and identify FOUR distinct problems that they might face, which may need design solutions. Write the FOUR problem statements starting with “How can we…â€. Select ANY ONE problem and propose TWO potential design solutions.
- CEED - 2026
- Sketching and Drawing
- Two objects created using a toy set are shown below. Choose the set of features that \textbf{CANNOT be attributed to the toy set.}
- CEED - 2026
- Quantitative Aptitude
View More Questions