Chapter-5 (Area And Volume) Important Questions

Area and Volume: Important Questions

Mathematics • Grade 10 • Area and Volume

A. Theory

2 marks1. Define pyramid. Write the formula of its LSA, TSA and volume (square base).

A solid with a polygonal base and triangular lateral faces meeting at one vertex. LSA = 2al, TSA = a² + 2al, V = ⅓a²h

3 marks2. Prove l² = h² + (a/2)² for a square based pyramid.

In the right-angled triangle formed by the vertical height h, the line from the centre of the base to the midpoint of a side (a/2), and the slant height l, Pythagoras gives l² = h² + (a/2)².

2 marks3. Write the formulas of CSA, TSA and volume of a cone. How are l, h, r related?

CSA = πrl, TSA = πr(r + l), V = ⅓πr²h; l² = h² + r²

2 marks4. How many cones fill a cylinder of equal base and height? What does this give?

Three. V(cone) = ⅓ × V(cylinder) = ⅓πr²h

3 marks5. Write TSA and volume formulas for (a) cone + hemisphere (b) cylinder + hemisphere.

(a) πr(l + 2r); ⅓πr²(h + 2r) (b) 2πrh + 3πr²; πr²(h + ⅔r)

B. Numerical

3 marks6. A square pyramid has a = 10 cm, e = 13 cm. Find TSA.

l = 12; TSA = 100 + 240 = 340 cm²

4 marks7. TSA = 144 cm², l = 5 cm. Find h and e.

a = 8; h = 3 cm, e = √41 cm

4 marks8. V = 384 cm³, a = 12 cm. Find LSA.

h = 8, l = 10; LSA = 240 cm²

4 marks9. A pyramid-shaped tent has a = 32 m, h = 50 m. Cloth needed and cost at Rs. 500/m²?

l = √2756 = 52.50; LSA = 3359.84 m²; cost = Rs. 16,79,923.81

4 marks10. Cone: h = 12 cm, l = 13 cm. Find base area and CSA.

r = 5; 78.57 cm²; 204.28 cm²

4 marks11. Sum of radius and slant height of a cone is 64 cm and TSA is 2816 cm². Find CSA.

r = 14, l = 50; CSA = 2200 cm²

4 marks12. V = 100π cm³, h = 12 cm. Find slant height.

r² = 25; l = 13 cm

5 marks13. Three cones of same height with radii 3, 4, 5 cm are melted into one cone of the same height. Find its diameter.

R² = 9 + 16 + 25 = 50; diameter = 10√2 cm

5 marks14. Pencil: r = 7 cm, cylinder 39 cm, cone 24 cm. Find TSA and V.

TSA = 2420 cm²; V = 7238 cm³

5 marks15. Ice cream r = 21 cm, V = 32340 cm³. Find cone height and TSA.

h = 28 cm; TSA = 5082 cm²

5 marks16. Stupa: prism 5 m, pyramid 0.5 m, a = 2 m. Find V and TSA.

V = 20.67 m³; TSA = 48.47 m²

5 marks17. Room 14 × 12 × 10 ft; 2 windows 3 ft square, 2 doors 6 × 2 ft. Cost of painting walls and ceiling at Rs. 30/ft²?

Area = 646 ft²; Rs. 19,380

5 marks18. Two pillars 4 × 4 ft, 10 ft high, pyramid 2 ft on top. Cost at Rs. 95/ft². Why is the base not included?

Rs. 34,701.60; the base lies on the ground, so it is not painted.

Area and Volume • Grade 10 Mathematics