1. Length, breadth and height of a cuboid shape box of medicine are 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.
Here, l = 20 cm, b = 12 cm, h = 10 cm
Surface area of vertical faces
= 2h(l + b)
= 2 × (20 + 12) × 10
∴ Surface area of vertical faces = 640 cm² ... (i)
Also,
Total surface area of a cuboid
= 2(lb + bh + hl)
= 2(20 × 12 + 12 × 10 + 10 × 20)
= 2(240 + 120 + 200)
= 2(560)
∴ Total surface area = 1120 cm² ... (ii)
∴ The surface area of vertical faces of this box is 640 cm² and its total surface area is 1120 cm²
2. Total surface area of a box of cuboid shape is 500 sq. unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box?
Here, S = 500 sq. unit, b = 6 unit, h = 5 unit, l = ?
Total surface area of a cuboid:
S = 2(lb + bh + hl)
∴ 500 = 2(l × 6 + 6 × 5 + 5 × l)
∴ 500 = 2(6l + 30 + 5l)
∴ 500 = 2(11l + 30)
∴ \(\displaystyle \frac {500}{2}\) = 11l + 30
∴ 250 = 11l + 30
∴ 250 - 30 = 11l
∴ 220 = 11l
∴ \(\displaystyle \frac {220}{11}\) = l
∴ 20 = l
i.e. l = 20 unit ... (i)
∴ The length of that box is 20 unit.
3. Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.
Here, l = 4.5 cm
Surface area of vertical faces of a cube
= 4l²
= 4 × 4.5 × 4.5
= 81.5 cm² ... (i)
Also,
Total surface area of a cube (St)
= 6l²
= 6 × 4.5 × 4.5
= 121.5 cm² ... (ii)
∴ The surface area of all vertical faces of the cube is 81.5 cm² and its total surface area is 121.5 cm².
4. Total surface area of a cube is 5400 sq. cm. Find the surface area of all vertical faces of the cube.
Here, S = 5400 cm², l = ?
Total surface area of a cube:
St = 6l²
∴ 5400 = 6l²
∴ \(\displaystyle \frac {5400}{6}\) = l²
∴ 900 = l²
i.e. l² = 900 ... (i)
Now,
Surface area of vertical faces of a cube
= 4l²
= 4 × 900 ... [From(i)]
= 3600 cm²
∴ The surface area of all vertical faces of the cube is 3600 cm².
5. Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5 m and 1.15 m respectively. Find its length.
Here, V = 34.50 m³, b = 1.5 m, h = 1.15 m, l = ?
Volume of a cuboid:
V = l × b × h
∴ 34.50 = l × 1.5 × 1.15
∴ \(\displaystyle \frac {34.50}{1.5 \times 1.15}\) = l
∴ \(\displaystyle \frac {34500}{15 \times 115}\) = l
∴ 20 = l
i.e. l = 20 m ... (i)
∴ The length of the cuboid is 20 m.
6. What will be the volume of a cube having length of edge 7.5 cm.?
Here, l = 7.5 cm, V = ?
Volume of a cube:
V = l³
∴ V = 7.5 × 7.5 × 7.5
∴ V = 421.875 ≈ 421.88 cm³
∴ The volume of the cube is 421.88 cm³.
7. Radius of base of a cylinder is 20 cm and its height is 13 cm, find its curved surface area and total surface area. (π = 3.14)
Here, r = 20 cm, h = 13 cm, Sc = ?, St = ?
Curved surface area of a cylinder:
Sc = 2πrh
∴ Sc = 2 × 3.14 × 20 × 13
∴ Sc = 1632.8 cm² ... (i)
And,
Total surface area of a :
St = 2πr(r + h)
∴ St = 2 × 3.14 × 20 (20 + 13)
∴ St = 2 × 3.14 × 20 × 33
∴ St = 4144.8 cm² ... (ii)
∴ The curved surface area of the cylinder is 1632.8 cm² and its total surface area is 4144.8 cm²
8. Curved surface area of a cylinder is 1980 cm² and radius of its base is 15 cm. Find the height of the cylinder. (π = \(\displaystyle \frac {22}{7}\))
Here, Sc = 1980 cm², r = 15 cm, h = ?
Curved surface area of a cylinder:
Sc = 2πrh
∴ 1980 = 2 × \(\displaystyle \frac {22}{7}\) × 15 × h
∴ \(\displaystyle \frac {1980 \times 7}{2 \times 22 \times 15}\) = h
∴ 21 = h
i.e. h = 21 cm ... (i)
∴ The height of the cylinder is 21 cm.
This page was last modified on
19 February 2026 at 11:08