Volume and Surface Area of Solid Figures
- The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 60 cm). ?
-
View Hint View Answer Discuss in Forum
Let the sides of the base are 5k, 12k and 13k, respectively.
Given, perimeter of base = 60 cm
⇒ 5k + 12k + 13k = 60Correct Option: A
Let the sides of the base are 5k, 12k and 13k, respectively.
Given, perimeter of base = 60 cm
⇒ 5k + 12k + 13k = 60
∴ k = 60/30 = 2
The sides of base are 10 cm, 24 cm 26 cm.
∴ Volume of prism = (1/2) x 10 x 24 x 50 = 6000 cm3
- A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid ?
-
View Hint View Answer Discuss in Forum
Volume of the prism = (Area of the base ) x (Height)
Volume of the pyramid = 1/3 (Area of the base ) x (Height)Correct Option: C
Volume of the prism = (Area of the base ) x (Height)
Volume of the pyramid = 1/3 (Area of the base ) x (Height)
Required ratio = [A x H] / [(1/3) x A x H]
Therefore, Ratio of the volumes of the prism and the pyramid = 3 : 1.
- The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surface of the cylinder to that of the cone is ?
-
View Hint View Answer Discuss in Forum
Ratio of curved surface area of cylinder and cone = [2πrh] / [πr√h2 + r2]
Correct Option: C
Ratio of curved surface area of cylinder and cone = [2πrh] / [πr√h2 + r2]
= [2 x 6 x 8] / [6 x √62 + 82]
= 96/(6 x 10) = 96/60 = 8/5 = 8 : 5
- A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is ?
-
View Hint View Answer Discuss in Forum
Let required number of coins be n, Then,
n x 1/3 x π (1/10)2 x 1 = π x (3)2 x 5Correct Option: B
Let required number of coins be n, Then,
n x 1/3 x π (1/10)2 x 1 = π x (3)2 x 5
∴ n = 9 x 5 x 3 x 100 = 13500
- How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each bullet being 4 cm in diameter ?
-
View Hint View Answer Discuss in Forum
Volume of 1 bullet = 4/3π(2)3 = (32/3 x 22/7) cm3
Volume of the cube = (44)3Correct Option: B
Volume of 1 bullet = 4/3π(2)3 = (32/3 x 22/7) cm3
Volume of the cube = (44)3
∴ Number of bullets = Volume of solid/Volume of 1 bullet
= (44)3 x 3 x 7 / 32 x 22 = 2541