Volume & Surface area of Solids

Q1: Fill in the blanks:

i. 1 m³ = ______ cm³.

Step 1: We know: \[ 1\, m = 100\, cm \] Hence, \[ 1\, m^3 = (100\, cm)^3 = 100^3\, cm^3 = 1,000,000\, cm^3 = 10^6\, cm^3 \] Answer:1 m³ = 1,000,000 cm³

ii. 1 cm³ = ______ dm³.

Step 2: We know: \[ 1\, dm = 10\, cm \] Hence, \[ 1\, cm^3 = \left(\frac{1}{10}\, dm\right)^3 = \frac{1}{1000}\, dm^3 = 0.001\, dm^3 \] Answer:1 cm³ = 0.001 dm³

iii. If the surface of a cube is numerically equal to its volume, then the edge of the cube is _______.

Step 3: Let the edge of the cube be \(a\). Given:
Surface area \(= 6a^2\)
Volume \(= a^3\)
Given that surface area \(= \) volume numerically: \[ 6a^2 = a^3 \\ a^3 – 6a^2 = 0 \\ a^2 (a – 6) = 0 \\ a = 0 \text{ or } a = 6 \] Edge length cannot be zero, so \[ a = 6 \] Answer:The edge of the cube is 6

iv. To calculate the area of the road paved by a road roller, we need to find the ________ of the roller .

Step 4: To find the area paved by the road roller, we need to find the curved surface area of the roller.
Answer:curved surface area

v. A ______ when rolled along its length or breadth forms a cylinder.

Step 5: A rectangle when rolled along its length or breadth forms a cylinder.
Answer:rectangle

vi. If the volume of a cylinder is numerically equal to its curved surface area, then the radius of its base is ______.

Step 6: Let radius = \(r\), height = \(h\). Given:
Volume \(V = \pi r^2 h\)
Curved Surface Area \(CSA = 2\pi r h\)
Given volume = curved surface area numerically: \[ \pi r^2 h = 2 \pi r h \] Divide both sides by \(\pi r h\) (assuming \(r, h \neq 0\)): \[ r = 2 \] Answer:The radius of the base is 2