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Surface Areas and Volumes

Madhya Pradesh Board · Class 10 · Mathematics

Flashcards for Surface Areas and Volumes — Madhya Pradesh Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

136 questions48 flashcards5 concepts

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An illustration showing common 3D geometric shapes (cuboid, cone, cylinder, sphere, hemisphere) and examples of real-world objects formed by combining these basic shapes, such as a truck container (cy
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48 Flashcards
Card 1Surface area of combined solids

A solid is a cylinder with two hemispheres attached at its ends. What is the total surface area?

Answer

Step 1: Only the curved parts are exposed. The flat circular faces are joined and not counted. Step 2: TSA of new solid = CSA of one hemisphere + CSA of cylinder + CSA of other hemisphere. Step 3: Sin…

Card 2संयोजित ठोसों का सतही क्षेत्रफल

एक ठोस एक बेलन है जिसके दोनों सिरों पर दो अर्धगोले जुड़े हैं। कुल सतही क्षेत्रफल क्या है?

Answer

चरण 1: केवल वक्र भाग खुले हैं। समतल वृत्ताकार पृष्ठ जुड़े हुए हैं और गिने नहीं जाते। चरण 2: नए ठोस का TSA = एक अर्धगोले का CSA + बेलन का CSA + दूसरे अर्धगोले का CSA. चरण 3: क्योंकि दोनों अर्धगोले समान…

Card 3Concept of exposed surface area

Why is the total surface area of a combined solid not always the sum of the total surface areas of its parts?

Answer

When two solids are joined, some flat surfaces disappear at the joint. Those joined faces are not exposed outside, so they are not counted. Example idea: In a solid made by joining shapes, only the vi…

Card 4खुले सतह क्षेत्रफल की अवधारणा

संयोजित ठोस का कुल सतही क्षेत्रफल हमेशा उसके भागों के कुल सतही क्षेत्रफलों का योग क्यों नहीं होता?

Answer

जब दो ठोस जुड़े होते हैं, तो जोड़ पर कुछ समतल पृष्ठ गायब हो जाते हैं। वे जुड़े हुए पृष्ठ बाहर खुले नहीं रहते, इसलिए उन्हें गिना नहीं जाता। उदाहरण का विचार: आकृतियों को जोड़कर बने ठोस में केवल दिखाई दे…

Card 5Surface area of cone and hemisphere toy

A toy is made by joining a hemisphere and a cone of the same radius. What formula is used for its total surface area?

Answer

Formula: Total surface area of the toy = CSA of hemisphere + CSA of cone. Here, the flat circular faces are joined, so they are not counted. If radius is r and cone slant height is l: CSA of hemispher…

Card 6शंकु और अर्धगोले वाले खिलौने का सतही क्षेत्रफल

एक खिलौना एक अर्धगोले और समान त्रिज्या वाले एक शंकु को जोड़कर बनाया गया है। इसके कुल सतही क्षेत्रफल के लिए कौन-सा सूत्र उपयोग किया जाता है?

Answer

सूत्र: खिलौने का कुल सतही क्षेत्रफल = अर्धगोले का CSA + शंकु का CSA. यहाँ, समतल वृत्ताकार पृष्ठ जुड़े हुए हैं, इसलिए उन्हें नहीं गिना जाता। यदि त्रिज्या r है और शंकु की तिर्यक ऊँचाई l है: अर्धगोले का …

Card 7Worked example on combined surface area

Solve: A top is shaped like a cone surmounted by a hemisphere. Total height = 5 cm and diameter = 3.5 cm. Find the area to be coloured. Take π = 22/7.

Answer

Step 1: Radius r = 3.5/2 = 1.75 cm. Step 2: Height of hemisphere = radius = 1.75 cm. Step 3: Height of cone = 5 - 1.75 = 3.25 cm. Step 4: Slant height l = √(r² + h²) = √(1.75² + 3.25²) ≈ 3.7 cm. Step …

Card 8संयोजित सतही क्षेत्रफल पर हल किया गया उदाहरण

हल करें: एक लट्टू का आकार एक अर्धगोले पर रखा हुआ शंकु है। कुल ऊँचाई = 5 cm और व्यास = 3.5 cm। रंगने के लिए क्षेत्रफल ज्ञात कीजिए। π = 22/7 लें।

Answer

चरण 1: त्रिज्या r = 3.5/2 = 1.75 cm. चरण 2: अर्धगोले की ऊँचाई = त्रिज्या = 1.75 cm. चरण 3: शंकु की ऊँचाई = 5 - 1.75 = 3.25 cm. चरण 4: तिर्यक ऊँचाई l = √(r² + h²) = √(1.75² + 3.25²) ≈ 3.7 cm. चरण 5: अर…

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Surface Areas and Volumes covers several key topics that are frequently asked in Madhya Pradesh Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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