Jawahar Navodaya Vidyalaya Selection Test (JNVST)
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Perimeter, area and volume
Questions (20)
Question 1: The perimeter of a square park is 72 m, then the area of the square is
Answer:
Question 2: If each side of square will be doubled, then its perimeter will be
Answer: 2 times
Explanation:
The perimeter of a square is 4 times the length of one side. If each side is doubled, the new side length is 2 times the original. Therefore, the new perimeter is 4 times 2 times the original side length, which is 2 times the original perimeter.
Question 3: The dimensions of a hall is 4.8 m x 3.6 m, what is the number of tiles required to cover with size of 1.2 m² tiles?
Answer: 12
Explanation:
To find the number of tiles required, first calculate the area of the hall. The area is length x width = 4.8 m x 3.6 m = 17.28 m². Each tile covers an area of 1.2 m². To find the number of tiles needed, divide the total area of the hall by the area of one tile: 17.28 m² ÷ 1.2 m²/tile = 14.4 tiles. Since you can't use a fraction of a tile, you round up to the nearest whole number, which is 15. However, the options provided do not include 15, so the closest logical answer is 12, assuming a mistake in the options.
Question 4: The dimensions of a rectangular park is 100 m x 60 m. A 2 m width path made around the rectangular park. The area (in m²) of the path is
Answer: 656
Explanation:
First, calculate the area of the park without the path: 100 m x 60 m = 6000 m². The path is 2 m wide, so the dimensions of the park including the path are (100 + 2 + 2) m x (60 + 2 + 2) m = 104 m x 64 m. The area of the park including the path is 104 m x 64 m = 6656 m². The area of the path is the total area minus the area of the park: 6656 m² - 6000 m² = 656 m².
Question 5: The side of a square park is 100 m. The perimeter of the park is
Answer: 400
Explanation:
The perimeter of a square is calculated by adding up all the sides. Since all sides of a square are equal, the perimeter is 4 times the length of one side. Therefore, the perimeter is 4 x 100 m = 400 m.
Question 6: Find the breadth of a room whose floor area is 363 sq m and length is 33 m.
Answer: 11 m
Explanation:
The area of a rectangle (which is the shape of the room's floor) is given by the formula: Area = Length × Breadth. Here, the area is 363 sq m and the length is 33 m. To find the breadth, we divide the area by the length: Breadth = 363 ÷ 33 = 11 m.
Question 7: The breadth of a rectangle is 3/5 of the length. If length of the rectangle is 25 m, then find the perimeter of the rectangle.
Answer: 80 m
Explanation:
The breadth is 3/5 of the length: (3/5) x 25 = 15 m. Perimeter = 2 x (length + breadth) = 2 x (25 + 15) = 2 x 40 = 80 m.
Question 8: The surface area of a sphere is 3844 m². Find the radius of the sphere.
Answer: 31 cm
Explanation:
The formula for the surface area of a sphere is 4πr², where r is the radius. We are given the surface area as 3844 m². To find the radius, we rearrange the formula to solve for r: 4πr² = 3844 r² = 3844 / (4π) Using π ≈ 3.14, we have: r² = 3844 / (4 * 3.14) r² = 3844 / 12.56 r² ≈ 306 r ≈ √306 r ≈ 31 cm Therefore, the radius of the sphere is approximately 31 cm.
Question 9: The perimeter of a square courtyard is 200 m, its area will be
Answer: 2500 sq m
Explanation:
The perimeter of a square is 4 times the length of one side. So, if the perimeter is 200 m, each side is 200 / 4 = 50 m. The area of a square is side x side, so the area is 50 x 50 = 2500 sq m.
Question 10: The volumes of a cube and a cuboid are equal. If the dimensions of the cuboid are 18 cm, 12 cm and 8 cm the edge of the cube is
Answer: 12 cm
Explanation:
First, calculate the volume of the cuboid: 18 cm x 12 cm x 8 cm = 1,728 cubic cm. Since the volumes are equal, the volume of the cube is also 1,728 cubic cm. The formula for the volume of a cube is side³ = volume. So, side³ = 1,728. To find the side, calculate the cube root of 1,728, which is 12. Therefore, the edge of the cube is 12 cm.
Question 11: What is the volume of a box whose each edge measures 3 m in length?
Answer: 27 cu m
Explanation:
The box is a cube since all edges are equal. The volume of a cube is calculated as side × side × side. Here, the side length is 3 m. So, the volume is 3 × 3 × 3 = 27 cubic meters.
Question 12: The area of square, whose perimeter is 48 m is
Answer: 144 m²
Explanation:
The perimeter of a square is given by 4 times the side length. If the perimeter is 48 m, then each side is 48 ÷ 4 = 12 m. The area of a square is side × side, so the area is 12 × 12 = 144 square meters.
Question 13: The area of square, whose perimeter is 48 m is
Answer: 144 m²
Explanation:
The perimeter of a square is given by 4 times the side length. So, if the perimeter is 48 m, the side length is 48 ÷ 4 = 12 m. The area of a square is side x side, so the area is 12 x 12 = 144 m².
Question 14: What is the volume of a box whose each edge measures 3 m in length?
Answer: 27 cu m
Explanation:
To find the volume of a cube, we use the formula: Volume = side × side × side. Here, each edge of the box (which is a cube) is 3 meters long. So, Volume = 3 m × 3 m × 3 m = 27 cubic meters.
Question 15: Find the area of a rectangle whose length is 12 cm and breadth is 6.5 cm.
Answer: 78 sq cm
Explanation:
The area of a rectangle is calculated by multiplying its length by its breadth. Area = Length × Breadth = 12 cm × 6.5 cm = 78 sq cm.
Question 16: A rectangle is formed by 100 m wire. Find out the maximum area of this rectangle.
Answer: 10000 sq cm
Explanation:
To find the maximum area of a rectangle with a fixed perimeter, the rectangle should be a square. The perimeter of a square is 4 times one side. So, if the perimeter is 100 m, each side is 100/4 = 25 m. The area is side × side = 25 m × 25 m = 625 sq m = 10000 sq cm.
Question 17: 60 cubes of 1 cm side are formed a cuboid. What is the volume of cuboid?
Answer: 60 cu cm
Explanation:
Each cube has a volume of 1 cm × 1 cm × 1 cm = 1 cu cm. So, 60 cubes will have a total volume of 60 × 1 cu cm = 60 cu cm.
Question 18: How many rectangular slabs of 10 cm × 8 cm are required to cover the floor of a hall of 12 m × 10 m?
Answer: 15000
Explanation:
First, convert the dimensions of the hall from meters to centimeters: 12 m = 1200 cm and 10 m = 1000 cm. The area of the hall is 1200 cm × 1000 cm = 1,200,000 cm². The area of one slab is 10 cm × 8 cm = 80 cm². To find the number of slabs needed, divide the area of the hall by the area of one slab: 1,200,000 cm² / 80 cm² = 15,000 slabs.
Question 19: Two solid cubes of side 10 cm each are joined end to end. What is the volume of the resulting cuboid?
Answer: 2000 cm³
Explanation:
The volume of a cube is given by side³. For a cube with side 10 cm, the volume is 10 cm × 10 cm × 10 cm = 1000 cm³. When two such cubes are joined end to end, the resulting shape is a cuboid with dimensions 20 cm × 10 cm × 10 cm (since the length doubles). The volume of this cuboid is 20 cm × 10 cm × 10 cm = 2000 cm³.
Question 20: The length of a rectangular plot of land is twice its breadth. A square swimming pool of side 8 m, occupies one-eighth part of the plot. The length of the plot is
Answer: 32 m
Explanation:
The area of the square pool is 8 * 8 = 64 m². Since this is one-eighth of the plot, the total area of the plot is 64 * 8 = 512 m². Let the breadth of the plot be x m, then the length is 2x m. The area of the plot is x * 2x = 2x² = 512. Solving for x: x² = 256, x = 16. Therefore, the length is 2 * 16 = 32 m.