Important Questions: Surface Areas & Volumes - Class 10 MCQ

A cubical ice cream brick of edge 22 cm is to be distributed among children by filling ice cream cones of radius 2 cm and height 7 cm. Let's calculate how many children can get ice cream cones.

Step 1: Volume of the Cubical Ice Cream Brick
The volume of a cube is given by:
Volume = edge³
Here, edge = 22 cm:
Volume = 22³ = 10648 cm³

Step 2: Volume of One Ice Cream Cone
The volume of a cone is given by:
Volume = (1/3) π r² h
Here, radius (r) = 2 cm and height (h) = 7 cm:
Volume = (1/3) π (2²) (7)
Volume = (1/3) π (4) (7) = (28/3) π cm³
Using π ≈ 3.1416:
Volume ≈ (28/3) × 3.1416 ≈ 29.32 cm³

Step 3: Number of Children
The number of children who can get cones is:
Number of children = Volume of cube / Volume of one cone
Number of children = 10648 / 29.32 ≈ 363
Answer: c) 363

Correct Option: (b) 1 → F, 2 → A, 3 → C, 4 → E

The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.

Edge of the cube = 4.2 cm

i.e 2r = 4.2

r = 4.2/2 = 2.1 cm

h = 4.2 cm

Volume of the cone = 1/3 * pi * r² * h

=> 1/3 * 22/7 * 2.1 * 2.1 * 4.2

=> 19.404 cm³

Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm³.

Edge of the cube = 4.2 cm
Diameter of base of largest possible cone = 4.2 cm
∴ Radius = 4.2/2 = 2.1 cm

Volume of water displaced = 150 x 8 = 1200 m³ 
⇒ 90 x 40 x h = 1200
⇒