Mensuration – 3D

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Home › PYQ Aptitude › PYQ Aptitude › Mensuration - 3D

Mensuration - 3D ▼

PYQ Aptitude — Topics

○ Age 1 ○ Average 1 ○ Boat and Stream 1 ○ Compound Interest 1 ○ Data Interpretation 1 ○ Discount (बट्टा) 1 ○ LCM & HCF 1 ● Mensuration - 3D 1 ○ Mensuration -2D 1 ○ Mixture & Alligation 1 ○ Number System 1 ○ Partnership 1 ○ Percentage Related PYQ's 1 ○ Pipe and Cistern 1 ○ Profit and Loss Related PYQ's 1 ○ Ratio and Proportion 1 ○ Simple Interest 1 ○ Simplification (सरलीकरण) 1 ○ Speed, Time & Distance 1 ○ Train 1 ○ Work and Time 1

📝 20 Questions

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Question 1

 If the height of a cylinder is 16 cm and radius 14 cm, find its curved surface area  \((in~cm^2)\). / यदि किसी बेलन की ऊँचाई 16 सेमी और त्रिज्या 14 सेमी है, तो उसका वक्र पृष्ठीय क्षेत्रफल ज्ञात कीजिए (सेमी² में)। {SSC GD 21 Feb 2025 Shift-II}

A 1418

B 1408

C 1412

D 1424

✔ Correct Answer: B — 1408

Explanation: बेलन का वक्र पृष्ठीय क्षेत्रफल =  \[ \begin{aligned}2\pi rh\\\\=2\times\frac{22}{7}\times14\times16\\\\=1408~cm^2\end{aligned} \] 

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Question 2

The radius of a sphere is 3.5 cm. What is the total surface area of the sphere? / एक गोले की त्रिज्या 3.5 सेंटीमीटर है। गोले का कुल पृष्ठीय क्षेत्रफल कितना है? {SSC GD 20 Feb 2024 Shift-IV}

A  \(196~cm^2\) 

B  \(154~cm^2\) 1

C  \(128~cm^2\) 

D  \(176~cm^2\) 

✔ Correct Answer: B —  \(154~cm^2\) 1

Explanation:  r = 3.5 cm

गोले का कुल पृष्ठीय क्षेत्रफल =  \[ \begin{aligned}4\pi r^2\\\\=4\times \frac{22}{7}\times3.5\times3.5\\\\=154~cm^2\end{aligned} \]

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Question 3

The internal radius of a hemispherical bowl made of brass is 3.5 cm. Find the cost of tin plating it inside at the rate of Rs. 4 per  \(cm^2\)  / पीतल से बने एक अर्धगोलाकार कटोरे की आंतरिक त्रिज्या 3.5 सेमी है। 4 रुपये प्रति सेमी² की दर से इसके भीतर टिन चढ़ाने की लागत ज्ञात कीजिए। {SSC GD 19 Feb 2025 Shift-I}

A 328

B 348

C 308

D 318

✔ Correct Answer: C — 308

Explanation:  अर्द्धगोले का वक्रपृष्ठ = \[ \begin{aligned}2\pi r^2\\\\=2\times\frac{22}{7}\times3.5\times3.5\\\\=77~cm^2\end{aligned} \] 

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Question 4

Find the area  \((in~cm^2)\) of card board required to make a box of size  \(12~cm\times14~cm\times8~cm.\)  / 12 सेमी × 14 सेमी × 8 सेमी आकार का डिब्बा बनाने के लिए आवश्यक कार्डबोर्ड का क्षेत्रफल ज्ञात कीजिए। {SSC GD 25 Feb 2025 Shift-II}

A 748

B 752

C 764

D 736

✔ Correct Answer: B — 752

Explanation:  संपूर्ण पृष्ठीय क्षेत्रफल (TSA) =  \[ \begin{aligned}2(lb+bh+hl)\\\\=2(12\times14+14\times8+8\times12)\\\\=2(168+112+96)\\\\=2\times376\\\\=752~cm^2\end{aligned} \]

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Question 5

What is the length of the longest pillar that can be placed in a room of dimensions  \(10m\times10m\times5m\)  ? / 10 मीटर × 10 मीटर × 5 मीटर आयाम वाले कमरे में रखे जा सकने वाले सबसे लंबे स्तंभ की लंबाई क्या है? {SSC GD 10 Jan 2023 Shift-II}

A 10m

B 20m

C 25m

D 15m

✔ Correct Answer: D — 15m

Explanation:  \[ \begin{aligned}l=10m\\\\b=10m\\\\h=5m\\\\length ~of~longest~pillar=\sqrt{l^2+b^2+h^2}\\\\=\sqrt{10^2+10^2+5^2}\\\\=\sqrt{225}=15m\end{aligned} \] 

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Question 6

What will be the volume of a sphere of radius  \(3\sqrt{2}~cm\) ? / \(3\sqrt{2}~cm\) सेमी त्रिज्या वाले गोले का आयतन क्या होगा? {SSC GD 10 Feb 2025 Shift-III}

A  \(70\sqrt{2}\pi~cm^3\) 

B  \(71\sqrt{2}\pi~cm^3\) 

C  \(73\sqrt{2}\pi~cm^3\) 

D  \(72\sqrt{2}\pi~cm^3\) 

✔ Correct Answer: D —  \(72\sqrt{2}\pi~cm^3\) 

Explanation: गोले का आयतन =  \[ \begin{aligned}\frac{4}{3}\pi r^2\\\\\frac{4}{3}\times \pi \times 3\sqrt{2}\times 3\sqrt{2}\times3\sqrt{2}\\\\=72\sqrt{2} \pi~cm^3\end{aligned} \] 

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Question 7

 The volume of a right circular cone is 168  \(\pi~cm^3\) and its height is 0.12m. Find its radius. / एक समकोण वृत्ताकार शंकु का आयतन 168(\pi~cm^3\) है और उसकी ऊँचाई 0.12 मीटर है। उसकी त्रिज्या ज्ञात कीजिए। {SSC GD 11 Feb 2025 Shift-II}

A  \(\sqrt{42}~cm\) 

B  \(\sqrt{41}~cm\) 

C  \(\sqrt{43}~cm\) 

D  \(\sqrt{47}~cm\) 

✔ Correct Answer: A —  \(\sqrt{42}~cm\) 

Explanation: शंकु का आयतन =  \[ \begin{aligned}\frac{1}{3} \pi r^2 h\\\\\frac{1}{3}\times \pi\times r^2\times 12=168~\pi\\\\r^2=42\\\\r=\sqrt{42}~cm\end{aligned} \] 

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Question 8

 The edge of a cube is 19 cm. Find the total Surface area (in  \(cm^2\)) of the cube. / एक घन की भुजा की लंबाई 19 सेमी है। घन का कुल पृष्ठीय क्षेत्रफल (सेमी² में) ज्ञात कीजिए। {SSC GD 6 Feb 2025 Shift-III}

A 2186

B 2156

C 2176

D 2166

✔ Correct Answer: D — 2166

Explanation: घन की कोर (a) = 19 cm

संपूर्ण पृष्ठीय क्षेत्रफल (TSA) =  \[ \begin{aligned}6a^2\\\\=6\times19\times19\\\\=2166~cm^2\end{aligned} \] 

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Question 9

A cube of side 9cm made of iron is melted and cast into 8 small cubes. Find the side (in cm) of each small cube. / लोहे से बने 9 सेमी भुजा वाले एक घन को पिघलाकर 8 छोटे घन बनाए जाते हैं। प्रत्येक छोटे घन की भुजा (सेमी में) ज्ञात कीजिए। {SSC GD 25 Feb 2025 Shift-I}

A 4

B 5

C 5.5

D 4.5

✔ Correct Answer: D — 4.5

Explanation: बड़े घन का आयतन =  \(n\times\)  छोटे घनों का आयतन

=  \[ \begin{aligned}9\times9\times9=8\times a\times a\times a\\\\a=\frac{9}{2}=4.5~cm\end{aligned} \] 

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Question 10

If the radius of a cylindrical tank is 7m and its height is 9m, find the capacity  \((in~m^3)\)  of the tank. / यदि एक बेलनाकार टंकी की त्रिज्या 7 मीटर और उसकी ऊँचाई 9 मीटर है, तो टंकी की क्षमता ज्ञात कीजिए। \((Use~\pi=\frac{22}{7})\)  {SSC GD 13 Feb 2025 Shift-III}

A 1386

B 1376

C 1396

D 1366

✔ Correct Answer: A — 1386

Explanation: बेलन का आयतन =  \[ \begin{aligned}\pi~r^2h\\\\=\frac{22}{7}\times7\times7\times9\\\\=1386~m^3\end{aligned} \] 

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