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Karnataka SSLC (Class 10) Mensuration: Surface Areas & Volumes — practice questions

Explore 90 free Mensuration: Surface Areas & Volumes questions in Karnataka SSLC (Class 10) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Mensuration: Surface Areas & Volumes questions and exercises with answers

Showing questions 1–30 of 90.

Area of a circle of radius r is:Read the answer and worked solution →Area of a sector subtending angle θ (deg) at the centre of a circle of radius r is:Read the answer and worked solution →Volume of a cone with radius r and height h is:Read the answer and worked solution →Volume of a sphere of radius r equals:Read the answer and worked solution →Match each solid to its total surface-area formula.Read the answer and worked solution →CLASS10 · Mathematics · Areas Related to CirclesRead the answer and worked solution →CLASS10 · Mathematics · Surface Area & VolumeRead the answer and worked solution →GST stands forRead the answer and worked solution →On intra-state sale GST is collected asRead the answer and worked solution →On inter-state sale GST is collected asRead the answer and worked solution →On a bill of Rs 1000 at 18% GST, the GST amount isRead the answer and worked solution →A trader sells goods worth Rs 2000 within the state at 12% GST. CGST and SGST each areRead the answer and worked solution →A wholesaler in Mumbai sells goods worth Rs 5000 to a dealer in Pune at 5% GST. The GST isRead the answer and worked solution →A trader in Delhi sells goods worth Rs 8000 to a customer in Jaipur at 18% GST. IGST isRead the answer and worked solution →Cost price Rs 1500 plus 12% GST. Total amount payable isRead the answer and worked solution →Input Tax Credit (ITC) lets a dealer claim credit forRead the answer and worked solution →A retailer buys an article at Rs 2000 + 18% GST and sells at Rs 2500 + 18% GST. Net GST deposited isRead the answer and worked solution →A shopkeeper in Lucknow buys at Rs 10000, then sells within Lucknow for Rs 12000, both at 12% GST. Net CGST he pays isRead the answer and worked solution →Marked price Rs 5000, discount 10%, then 18% GST. Amount payable isRead the answer and worked solution →Two articles cost Rs 800 and Rs 1200 each at 5% GST. Total amount payable isRead the answer and worked solution →Chennai dealer sells goods worth Rs 6000 to a Bengaluru dealer at 28% GST. IGST isRead the answer and worked solution →Marked price Rs 20000, discount 15%, then 18% GST. Amount payable isRead the answer and worked solution →Shopkeeper buys at Rs 4000 + 12% GST and sells within state at Rs 5000 + 12% GST. Net SGST payable isRead the answer and worked solution →Restaurant bill Rs 1200 with 5% GST. Total payable isRead the answer and worked solution →Selling price including 18% GST is Rs 2360. The price excluding GST isRead the answer and worked solution →Trader buys at Rs 10000 + 5% GST and sells at Rs 11000 + 5% GST in same state. Net GST payable isRead the answer and worked solution →Shopkeeper sells an article at Rs 4480 inclusive of 12% GST. Taxable value isRead the answer and worked solution →The formula for the area of a sector of a circle of radius r and angle theta (in degrees) isRead the answer and worked solution →The formula for the length of an arc of a circle of radius r and angle theta (in degrees) isRead the answer and worked solution →A sector with central angle 90 degrees in a circle of radius 14 cm has areaRead the answer and worked solution →

Worked practice questions

Area of a circle of radius r is:

  1. π r²
  2. 2 π r
  3. π r
  4. 2 r²
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Correct answer: A. π r²

To find the area of a circle, we use the standard geometric formula that relates the radius of the circle to the space it occupies on a 2D plane. 1. **Identify the Radius**: The radius is given as $r$, which is the distance from the center of the circle to its edge. 2. **Recall the Formula**: The area $A$ of a circle is calculated by taking the square of the radius ($r^2$) and multiplying it by the constant $\pi$ (approximately 3.14159). 3. **Set up the Equation**: $$A = \pi \times r^2$$ 4. **Conclusion**: The correct expression for the area is $\pi r^2$. Note: $2\pi r$ is the formula for the **circumference** (the distance around the circle), not the area.

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Area of a sector subtending angle θ (deg) at the centre of a circle of radius r is:

  1. (θ/180) × π r²
  2. (θ/360) × π r²
  3. π r²
  4. θ × r
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Correct answer: B. (θ/360) × π r²

To find the area of a sector of a circle, we follow these steps: 1. **Total Area**: The total area of a circle with radius $r$ is given by the formula: $$A_{total} = \pi r^2$$ 2. **Total Angle**: A complete circle subtends an angle of $360^\circ$ at its center. 3. **Proportionality**: A sector is a fraction of the entire circle. The ratio of the area of the sector to the total area of the circle is the same as the ratio of the angle subtended by the sector ($\theta$) to the total angle of the circle ($360^\circ$). $$\frac{\text{Area of Sector}}{\text{Total Area}} = \frac{\theta}{360^\circ}$$ 4. **Derivation**: Multiply both sides by the total area: $$\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2$$ Thus, the area of the sector is $(\theta/360) \times \pi r^2$.

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Volume of a cone with radius r and height h is:

  1. (2/3) π r² h
  2. π r² h
  3. (1/3) π r² h
  4. π r h
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Correct answer: C. (1/3) π r² h

To find the volume of a cone, we compare it to a cylinder with the same radius $r$ and height $h$. 1. **Base Area**: The base of a cone is a circle. The area of this base is given by the formula: $$A = \pi r^2$$ 2. **Relationship to a Cylinder**: A cylinder with the same dimensions has a volume of $V_{cylinder} = \text{Base Area} \times \text{Height} = \pi r^2 h$. 3. **The Cone Factor**: In geometry, it is proven (through calculus or physical displacement experiments) that a cone occupies exactly one-third of the volume of a cylinder with the same base and height. 4. **Final Formula**: Multiplying the cylinder volume by $1/3$, we get: $$V = \frac{1}{3} \pi r^2 h$$ Therefore, the correct option is **(1/3) π r² h**.

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