Q1.
What is the total surface area of a cuboid with length 8 cm, breadth 6 cm, and height 5 cm?
- 236 cm²
- 118 cm²
- 240 cm²
- 188 cm²
Show answer
Answer: A. 236 cm²
The total surface area of a cuboid is given by the formula 2(lb + bh + hl). Given l=8 cm, b=6 cm, h=5 cm. TSA = 2((8*6) + (6*5) + (5*8)) = 2(48 + 30 + 40) = 2(118) = 236 cm².
Q2.
What is the lateral surface area of a cube with side length 'a'?
- 6a²
- a³
- 4a²
- 2a²
Show answer
Answer: C. 4a²
The lateral surface area of a cube is the area of its four walls, which is 4 times the area of one face. So, LSA = 4a².
Q3.
A room is 10 m long, 8 m wide, and 4 m high. Find the cost of whitewashing its walls at Rs 5 per square meter.
- Rs 720
- Rs 360
- Rs 1440
- Rs 1800
Show answer
Answer: B. Rs 360
The area of the four walls (lateral surface area) of the room is 2h(l+b). Given l=10m, b=8m, h=4m. LSA = 2*4*(10+8) = 8*18 = 144 m². Cost of whitewashing = Area * Rate = 144 * 5 = Rs 720.
Q4.
Based on the bar chart, which solid has the largest surface area?
- Cuboid
- Cube
- Cylinder
- Cone
Show answer
Answer: A. Cuboid
From the bar chart, the surface areas are: Cuboid = 236 cm², Cube = 216 cm², Cylinder = 188 cm², Cone = 141 cm². The cuboid has the largest surface area.
Q5.
Find the curved surface area (CSA) of a cylinder with radius (r) = 7 cm and height (h) = 10 cm. (Use π = 22/7)
- 440 cm²
- 220 cm²
- 308 cm²
- 748 cm²
Show answer
Answer: A. 440 cm²
The curved surface area of a cylinder is given by the formula 2πrh. Given r=7 cm, h=10 cm. CSA = 2 * (22/7) * 7 * 10 = 2 * 22 * 10 = 440 cm².
Q6.
A cone has a radius of 3 cm and a height of 4 cm. What is its slant height (l)?
- 6 cm
- 5 cm
- 7 cm
- √7 cm
Show answer
Answer: B. 5 cm
The slant height (l) of a cone is given by the formula l = √(r² + h²). Given r=3 cm, h=4 cm. l = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.
Q7.
Find the total surface area (TSA) of a cylinder with radius 7 cm and height 14 cm. (Use π = 22/7)
- 748 cm²
- 616 cm²
- 924 cm²
- 1078 cm²
Show answer
Answer: C. 924 cm²
The total surface area of a cylinder is given by the formula 2πr(r + h). Given r=7 cm, h=14 cm. TSA = 2 * (22/7) * 7 * (7 + 14) = 2 * 22 * 21 = 44 * 21 = 924 cm².
Q8.
According to the pie chart showing mensuration topics weightage, which two topics have equal weightage?
- Cylinder and Cone
- Cone and Sphere
- Cuboid and Sphere
- Cone and Cuboid
Show answer
Answer: D. Cone and Cuboid
From the pie chart: Cylinder = 30%, Cone = 25%, Cuboid = 25%, Sphere = 20%. Cone and Cuboid both have 25% weightage.
Q9.
Find the surface area of a sphere with radius (r) = 14 cm. (Use π = 22/7)
- 616 cm²
- 1232 cm²
- 2464 cm²
- 5544 cm²
Show answer
Answer: C. 2464 cm²
The surface area of a sphere is given by the formula 4πr². Given r=14 cm. Surface Area = 4 * (22/7) * 14 * 14 = 4 * 22 * 2 * 14 = 88 * 28 = 2464 cm².
Q10.
What is the difference between the total surface area of a sphere and the total surface area of a hemisphere of the same radius 'r'?
- πr²
- 2πr²
- 3πr²
- 4πr²
Show answer
Answer: B. 2πr²
Total surface area of a sphere = 4πr². Total surface area of a hemisphere = 3πr². Difference = 4πr² - 3πr² = πr².
Q11.
Find the curved surface area (CSA) of a hemisphere with radius 7 cm. (Use π = 22/7)
- 154 cm²
- 308 cm²
- 462 cm²
- 616 cm²
Show answer
Answer: B. 308 cm²
The curved surface area of a hemisphere is given by the formula 2πr². Given r=7 cm. CSA = 2 * (22/7) * 7 * 7 = 2 * 22 * 7 = 44 * 7 = 308 cm².
Q12.
A toy is in the form of a cone mounted on a hemisphere of the same radius. If the radius is 3.5 cm and the total height of the toy is 15.5 cm, find the total surface area of the toy. (Use π = 22/7)
- 204.5 cm²
- 224.5 cm²
- 231 cm²
- 214.5 cm²
Show answer
Answer: D. 214.5 cm²
Radius (r) = 3.5 cm. Total height = 15.5 cm. Height of hemispherical part = r = 3.5 cm. Height of conical part (h) = Total height - r = 15.5 - 3.5 = 12 cm. Slant height of cone (l) = √(r² + h²) = √(3.5² + 12²) = √(12.25 + 144) = √156.25 = 12.5 cm. Total Surface Area of toy = CSA of cone + CSA of hemisphere = πrl + 2πr² = πr(l + 2r). TSA = (22/7) * 3.5 * (12.5 + 2*3.5) = 11 * (12.5 + 7) = 11 * 19.5 = 214.5 cm².
Q13.
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. (Use π = 22/7)
- 52.8 m²
- 35.2 m²
- 44 m²
- 61.6 m²
Show answer
Answer: C. 44 m²
Radius of cylindrical part (r) = Diameter/2 = 4/2 = 2 m. Height of cylindrical part (h_cyl) = 2.1 m. Slant height of conical part (l) = 2.8 m. Area of canvas = CSA of cylinder + CSA of cone = 2πrh_cyl + πrl = πr(2h_cyl + l). Area = (22/7) * 2 * (2*2.1 + 2.8) = (44/7) * (4.2 + 2.8) = (44/7) * 7 = 44 m².
Q14.
Based on the bar chart, which combination of solids has the highest number of problems?
- Cone+Sphere
- Cylinder+Hemisphere
- Cuboid+Pyramid
- Cylinder+Cone
Show answer
Answer: D. Cylinder+Cone
From the bar chart: Cone+Sphere = 8 problems, Cylinder+Cone = 12 problems, Cylinder+Hemisphere = 10 problems, Cuboid+Pyramid = 6 problems. Cylinder+Cone has the highest number of problems (12).
Q15.
A solid is composed of a cylinder with two hemispheres stuck at each end. If the radius of the cylinder and hemispheres is 'r' and the height of the cylindrical part is 'h', what is the total surface area of the solid?
- 2πr(h+r)
- 4πr(h+r)
- πr(h+2r)
- 2πr(h+2r)
Show answer
Answer: D. 2πr(h+2r)
The total surface area of the solid is the sum of the curved surface area of the cylinder and the curved surface areas of the two hemispheres. TSA = CSA_cylinder + 2 * CSA_hemisphere = 2πrh + 2 * (2πr²) = 2πrh + 4πr² = 2πr(h + 2r).
