What will be the volume of air enclosed in a conical tent of 6m height, enclosing 200 sq.m of ground?
(A) 800 cu.m
(B) 400 cu.m
(C) 600 cu.m
(D) 300 cu.m
In an ice cream cone, the radius of the base of the cone is 5 cm and slant height is 9 cm. Find the total surface area of the ice cream cone.
(A) 160 cm²
(B) 120 cm²
(C) 260 cm²
(D) 220 cm²
Nike announced a new design of football for the upcoming football tournament. If the radius of the new ball is 10 cm then find the surface area of the ball.
(A) 300π cm²
(B) 500π cm²
(C) 400π cm²
(D) 600π cm²
If the diameter of a sphere shaped box is 12 cm, then find the volume of the box.
(A) 225π cm³
(B) 121π cm³
(C) 169π cm³
(D) 144π cm³
Answer (1)
Let's solve each of these mathematical problems step-by-step:
Volume of Air in a Conical Tent:
We have the height h = 6 m and the area of the base A = 200 sq.m .
For a cone, the base area A = π r 2 . Here, r is the radius which we need to find using the given area. 200 = π r 2 r 2 = π 200
The volume V of a cone is given by: V = 3 1 π r 2 h V = 3 1 × 200 × 6 V = 400 cu.m
Answer: (B) 400 cu.m
Total Surface Area of the Ice Cream Cone:
The radius r = 5 cm and slant height l = 9 cm .
Total surface area A of a cone is the sum of the base area and the lateral surface area: A = π r ( r + l ) A = π × 5 ( 5 + 9 ) A = π × 5 × 14 A = 70 π cm 2 ≈ 219.91 cm 2
Answer: (D) 220 cm²
Surface Area of the Nike Football:
The radius r = 10 cm .
The surface area A of a sphere is: A = 4 π r 2 A = 4 π × 1 0 2 A = 400 π cm 2
Answer: (C) 400π cm²
Volume of the Sphere-shaped Box:
The diameter is 12 cm, so the radius r = 2 12 = 6 cm .
The volume V of a sphere is: V = 3 4 π r 3 V = 3 4 π × 6 3 V = 3 4 π × 216 V = 288 π cm 3
Answer: None of the given options are correct (correct volume is 288π cm³).
