Volume and Surface Area: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 3)

Let radius = r = 49 cm. Surface area of a sphere = 4 x pi x r^2. r^2 = 49 x 49 = 2401. 4 x 22 = 88, and 88 x 2401 = 211288. Dividing by 7: 211288 / 7 = 30184 sq cm.

Let radius = r = 70 cm. Surface area of a sphere = 4 x pi x r^2. r^2 = 70 x 70 = 4900. 4 x 22 = 88, and 88 x 4900 = 431200. Dividing by 7: 431200 / 7 = 61600 sq cm.

Let radius = r = 21 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 21 x 21 x 21 = 9261. 4 x 22 = 88, and 88 x 9261 = 814968. Dividing by 3 x 7 = 21: 814968 / 21 = 38808 cubic cm.

Let radius = r = 189 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 189 x 189 x 189 = 6751269. 4 x 22 = 88, and 88 x 6751269 = 594111672. Dividing by 3 x 7 = 21: 594111672 / 21 = 28291032 cubic cm.

Let radius = r = 42 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 42 x 42 x 42 = 74088. 4 x 22 = 88, and 88 x 74088 = 6519744. Dividing by 3 x 7 = 21: 6519744 / 21 = 310464 cubic cm.

Let radius = r = 84 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 84 x 84 x 84 = 592704. 4 x 22 = 88, and 88 x 592704 = 52157952. Dividing by 3 x 7 = 21: 52157952 / 21 = 2483712 cubic cm.

Let radius = r = 63 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 63 x 63 x 63 = 250047. 4 x 22 = 88, and 88 x 250047 = 22004136. Dividing by 3 x 7 = 21: 22004136 / 21 = 1047816 cubic cm.

Let radius = r = 231 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 231 x 231 x 231 = 12326391. 4 x 22 = 88, and 88 x 12326391 = 1084722408. Dividing by 3 x 7 = 21: 1084722408 / 21 = 51653448 cubic cm.

Let radius = r = 210 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 210 x 210 x 210 = 9261000. 4 x 22 = 88, and 88 x 9261000 = 814968000. Dividing by 3 x 7 = 21: 814968000 / 21 = 38808000 cubic cm.

Let radius = r = 105 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 105 x 105 x 105 = 1157625. 4 x 22 = 88, and 88 x 1157625 = 101871000. Dividing by 3 x 7 = 21: 101871000 / 21 = 4851000 cubic cm.

Let radius = r = 147 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 147 x 147 x 147 = 3176523. 4 x 22 = 88, and 88 x 3176523 = 279534024. Dividing by 3 x 7 = 21: 279534024 / 21 = 13311144 cubic cm.

Let radius = r = 126 cm. Volume of a sphere = (4/3) x pi x r^3. r^3 = 126 x 126 x 126 = 2000376. 4 x 22 = 88, and 88 x 2000376 = 176033088. Dividing by 3 x 7 = 21: 176033088 / 21 = 8382528 cubic cm.

Let base radius = r = 42 cm and height = h = 56 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 1764, h^2 = 3136. r^2 + h^2 = 1764 + 3136 = 4900. l = sqrt(4900) = 70 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 42 x 70 = 9240 sq cm.

Let base radius = r = 35 cm and height = h = 12 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 1225, h^2 = 144. r^2 + h^2 = 1225 + 144 = 1369. l = sqrt(1369) = 37 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 35 x 37 = 4070 sq cm.

Let base radius = r = 7 cm and height = h = 24 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 49, h^2 = 576. r^2 + h^2 = 49 + 576 = 625. l = sqrt(625) = 25 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 7 x 25 = 550 sq cm.

Let base radius = r = 28 cm and height = h = 45 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 784, h^2 = 2025. r^2 + h^2 = 784 + 2025 = 2809. l = sqrt(2809) = 53 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 28 x 53 = 4664 sq cm.

Let base radius = r = 70 cm and height = h = 24 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 4900, h^2 = 576. r^2 + h^2 = 4900 + 576 = 5476. l = sqrt(5476) = 74 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 70 x 74 = 16280 sq cm.

Let base radius = r = 14 cm and height = h = 48 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 196, h^2 = 2304. r^2 + h^2 = 196 + 2304 = 2500. l = sqrt(2500) = 50 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 14 x 50 = 2200 sq cm.

Let base radius = r = 21 cm and height = h = 28 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 441, h^2 = 784. r^2 + h^2 = 441 + 784 = 1225. l = sqrt(1225) = 35 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 21 x 35 = 2310 sq cm.

Let base radius = r = 28 cm and height = h = 96 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 784, h^2 = 9216. r^2 + h^2 = 784 + 9216 = 10000. l = sqrt(10000) = 100 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 28 x 100 = 8800 sq cm.

Let base radius = r = 56 cm and height = h = 90 cm. First find slant height l using l = sqrt(r^2 + h^2). r^2 = 3136, h^2 = 8100. r^2 + h^2 = 3136 + 8100 = 11236. l = sqrt(11236) = 106 cm. Curved surface area of a cone = pi x r x l. = (22/7) x 56 x 106 = 18656 sq cm.

Let base radius = r = 70 cm and height = h = 24 cm. Volume of a cone = (1/3) x pi x r^2 x h, one-third of the matching cylinder. r^2 = 70 x 70 = 4900. Base area = pi x r^2 = (22/7) x 4900 = 15400 sq cm. Base area x height = 15400 x 24 = 369600. One-third of that = 369600 / 3 = 123200 cubic cm.

Let base radius = r = 28 cm and height = h = 96 cm. Volume of a cone = (1/3) x pi x r^2 x h, one-third of the matching cylinder. r^2 = 28 x 28 = 784. Base area = pi x r^2 = (22/7) x 784 = 2464 sq cm. Base area x height = 2464 x 96 = 236544. One-third of that = 236544 / 3 = 78848 cubic cm.

Let base radius = r = 42 cm and height = h = 56 cm. Volume of a cone = (1/3) x pi x r^2 x h, one-third of the matching cylinder. r^2 = 42 x 42 = 1764. Base area = pi x r^2 = (22/7) x 1764 = 5544 sq cm. Base area x height = 5544 x 56 = 310464. One-third of that = 310464 / 3 = 103488 cubic cm.

Let base radius = r = 7 cm and height = h = 24 cm. Volume of a cone = (1/3) x pi x r^2 x h, one-third of the matching cylinder. r^2 = 7 x 7 = 49. Base area = pi x r^2 = (22/7) x 49 = 154 sq cm. Base area x height = 154 x 24 = 3696. One-third of that = 3696 / 3 = 1232 cubic cm.