Exam Questions & Step-by-Step Markschemes (4 Problems)
Question 1 • 2024
4 Marks
A solid wooden toy is in the shape of a cone mounted on a hemisphere with a common base of radius 7\text{ cm} . The total height of the toy is 31\text{ cm} . Find the total surface area of the toy. (Take \pi = 22/7 )
Answer: \text{Total Surface Area} = 858\text{ cm}^2
Question 2 • 2024
4 Marks
A metallic hollow cylindrical pipe of length 14\text{ cm} has an outer diameter of 10\text{ cm} and an inner diameter of 6\text{ cm} . Find the volume of metal contained in the pipe and the total surface area of the pipe. (Take \pi = 22/7 )
Answer: \text{Volume} = 704\text{ cm}^3, \quad \text{TSA} = \frac{5632}{7} \approx 804.57\text{ cm}^2
Question 3 • 2024
3 Marks
A metallic solid cone of height 24\text{ cm} and base radius 6\text{ cm} is melted and reshaped into the shape of a solid sphere. Find the radius of the sphere.
Answer: R = 6\text{ cm}
Question 4 • 2024
4 Marks
A solid metallic cylinder of diameter 12\text{ cm} and height 28\text{ cm} is melted and recast into a certain number of identical solid spheres of radius 3\text{ cm} . Find the number of spheres formed.
Answer: n = 28 \text{ spheres}