Riya made a container using metal sheets such that the container is in the shape of cuboid surmounted by a half cylinder. If the base of the container is of dimensions 30 cm × 14 cm, and the height of the cuboidal portion is 16 cm. She used this container to keep small boxes of volume 210 cm³ each.
Based on the above information, answer the following questions:
(a) How much total area of the sheet is used by her to make the container?
(b) How much air can be hold by the container?
(c) How many small boxes can store inside the container?
HERE
Diameter of half cylinder = 14cm
Radius of half cylinder = 7cm
Length (height) of half cylinder = 30 cm
Length of cuboid = 30cm
Breadth of cuboid = 14cm
Height of cuboid = 16cm
answer kya hai
a 2222 cm cube
To find the answers to the given questions, we need to calculate various measurements and use formulas for surface area, volume, and number of small boxes.
(a) To find the total area of the sheet used by Riya to make the container, we need to calculate the surface area of both the cuboid and the half cylinder.
Surface area of the cuboid = 2 * (length * breadth + length * height + breadth * height)
Surface area of the cuboid = 2 * (30 cm * 14 cm + 30 cm * 16 cm + 14 cm * 16 cm)
To calculate the surface area of the half cylinder, we first need to find the curved surface area of the cylinder and then divide it by 2 since it is only half a cylinder.
Curved surface area of the cylinder = 2 * π * radius * height
Curved surface area of the cylinder = 2 * π * 7 cm * 30 cm
Now, divide the curved surface area of the cylinder by 2 to get the surface area of the half cylinder.
Surface area of the half cylinder = (2 * π * 7 cm * 30 cm) / 2
Finally, add the surface area of the cuboid and the surface area of the half cylinder to find the total area of the sheet used.
Total area of the sheet = Surface area of the cuboid + Surface area of the half cylinder
(b) To find the volume of air that can be held by the container, we need to calculate the sum of the volume of the cuboid and the volume of the half cylinder.
Volume of the cuboid = length * breadth * height
Volume of the cuboid = 30 cm * 14 cm * 16 cm
To find the volume of the half cylinder, we need to subtract the volume of the cylinder from the volume of the cone and then divide it by 2 since it is only half a cylinder.
Volume of the cylinder = π * radius² * height
Volume of the cone = (1/3) * π * radius² * height
Now, subtract the volume of the cylinder from the volume of the cone and divide it by 2 to get the volume of the half cylinder.
Volume of the half cylinder = [(1/3) * π * 7 cm * 7 cm * 30 cm - π * 7 cm * 7 cm * 30 cm] / 2
Finally, add the volume of the cuboid and the volume of the half cylinder to find the total volume of air that can be held by the container.
Total volume of air = Volume of the cuboid + Volume of the half cylinder
(c) To find the number of small boxes that can be stored inside the container, we need to divide the volume of the container by the volume of each small box.
Number of small boxes = Total volume of air / Volume of each small box
Now, substitute the values of the given dimensions in the above calculations to get the final numerical answers for all the questions.