Volume and Surface Area: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 5)

Let radius = r = 84 cm and height = h = 28 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 84 x 84 = 7056. Base area = pi x r^2 = (22/7) x 7056 = 22176 sq cm. Volume = base area x height = 22176 x 28 = 620928 cubic cm.

Let radius = r = 49 cm and height = h = 17 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 49 x 49 = 2401. Base area = pi x r^2 = (22/7) x 2401 = 7546 sq cm. Volume = base area x height = 7546 x 17 = 128282 cubic cm.

Let radius = r = 42 cm and height = h = 5 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 42 x 42 = 1764. Base area = pi x r^2 = (22/7) x 1764 = 5544 sq cm. Volume = base area x height = 5544 x 5 = 27720 cubic cm.

Let radius = r = 91 cm and height = h = 6 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 91 x 91 = 8281. Base area = pi x r^2 = (22/7) x 8281 = 26026 sq cm. Volume = base area x height = 26026 x 6 = 156156 cubic cm.

Let radius = r = 14 cm and height = h = 17 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 14 x 14 = 196. Base area = pi x r^2 = (22/7) x 196 = 616 sq cm. Volume = base area x height = 616 x 17 = 10472 cubic cm.

Let radius = r = 63 cm and height = h = 25 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 63 x 63 = 3969. Base area = pi x r^2 = (22/7) x 3969 = 12474 sq cm. Volume = base area x height = 12474 x 25 = 311850 cubic cm.

Let radius = r = 105 cm and height = h = 9 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 105 x 105 = 11025. Base area = pi x r^2 = (22/7) x 11025 = 34650 sq cm. Volume = base area x height = 34650 x 9 = 311850 cubic cm.

Let radius = r = 14 cm and height = h = 15 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 14 x 14 = 196. Base area = pi x r^2 = (22/7) x 196 = 616 sq cm. Volume = base area x height = 616 x 15 = 9240 cubic cm.

Let radius = r = 70 cm and height = h = 4 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 70 x 70 = 4900. Base area = pi x r^2 = (22/7) x 4900 = 15400 sq cm. Volume = base area x height = 15400 x 4 = 61600 cubic cm.

Let radius = r = 77 cm and height = h = 8 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 77 x 77 = 5929. Base area = pi x r^2 = (22/7) x 5929 = 18634 sq cm. Volume = base area x height = 18634 x 8 = 149072 cubic cm.

Let radius = r = 84 cm and height = h = 24 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 84 x 84 = 7056. Base area = pi x r^2 = (22/7) x 7056 = 22176 sq cm. Volume = base area x height = 22176 x 24 = 532224 cubic cm.

Let radius = r = 105 cm and height = h = 10 cm. Volume of a cylinder = pi x r^2 x h. r^2 = 105 x 105 = 11025. Base area = pi x r^2 = (22/7) x 11025 = 34650 sq cm. Volume = base area x height = 34650 x 10 = 346500 cubic cm.

Let the three cube edges be a1 = 3 cm, a2 = 5 cm, a3 = 4 cm. Melting and recasting conserves total volume. a1^3 = 27, a2^3 = 125, a3^3 = 64 cubic cm. Total volume = 27 + 125 + 64 = 216 cubic cm. This is a perfect cube, so new edge = cube root of 216 = 6 cm. Surface area of new cube = 6 x edge^2 = 6 x 6^2. 6^2 = 36, so surface area = 6 x 36 = 216 sq cm. Check: 6^3 = 216, matching the total volume 216.

Let the three cube edges be a1 = 3 cm, a2 = 5 cm, a3 = 4 cm. Melting and recasting conserves total volume. a1^3 = 27, a2^3 = 125, a3^3 = 64 cubic cm. Total volume = 27 + 125 + 64 = 216 cubic cm. Since 216 is a perfect cube, new edge = cube root of 216. New edge = 6 cm. Check: 6^3 = 216, matching the total volume 216.

Let the edge of the cube = a = 26 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 26 x 26 = 676. Surface area = 6 x 676 = 4056 sq cm.

Let the edge of the cube = a = 15 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 15 x 15 = 225. Surface area = 6 x 225 = 1350 sq cm.

Let the edge of the cube = a = 11 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 11 x 11 = 121. Surface area = 6 x 121 = 726 sq cm.

Let the edge of the cube = a = 28 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 28 x 28 = 784. Surface area = 6 x 784 = 4704 sq cm.

Let the edge of the cube = a = 13 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 13 x 13 = 169. Surface area = 6 x 169 = 1014 sq cm.

Let the edge of the cube = a = 14 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 14 x 14 = 196. Surface area = 6 x 196 = 1176 sq cm.

Let the edge of the cube = a = 21 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 21 x 21 = 441. Surface area = 6 x 441 = 2646 sq cm.

Let the edge of the cube = a = 12 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 12 x 12 = 144. Surface area = 6 x 144 = 864 sq cm.

Let the edge of the cube = a = 4 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 4 x 4 = 16. Surface area = 6 x 16 = 96 sq cm.

Let the edge of the cube = a = 8 cm. A cube has 6 identical square faces, so total surface area = 6 x a^2. a^2 = 8 x 8 = 64. Surface area = 6 x 64 = 384 sq cm.

Let the edge of the cube = a, with volume = 12167 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 12167 = 23 cm. Check: 23^3 = 23 x 23 x 23 = 12167, which matches 12167.